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Analytic number theory
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fundamental differences in technique. Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number ofSmooth number (1,253 words) [view diff] no match in snippet view article find links to article

In number theory, a smooth (or friable) number is an integer which factors completely into small prime numbers. For example, a 7-smooth number is a numberPrime number theorem (5,673 words) [view diff] no match in snippet view article find links to article

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizesDiophantine approximation (3,755 words) [view diff] no match in snippet view article find links to article

In number theory, the field of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after DiophantusRandom number generation (3,833 words) [view diff] no match in snippet view article find links to article

numbers of any desired distribution by passing them through the inverse cumulative distribution function (CDF) of the desired distribution (see Inverse transformNatural number (3,935 words) [view diff] no match in snippet view article find links to article

natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, suchSupersingular prime (for an elliptic curve) (328 words) [view diff] no match in snippet view article

In algebraic number theory, a supersingular prime is a prime number with a certain relationship to a given elliptic curve. If the curve E defined overRandom matrix (3,422 words) [view diff] no match in snippet view article find links to article

results. In number theory, the distribution of zeros of the Riemann zeta function (and other L-functions) is modelled by the distribution of eigenvaluesHarmonic analysis (1,111 words) [view diff] no match in snippet view article find links to article

has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidalPrime number (13,507 words) [view diff] no match in snippet view article find links to article

numbers (2 × 3) that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural numberList of complex analysis topics (357 words) [view diff] no match in snippet view article find links to article

complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamicsSquare-free integer (2,223 words) [view diff] no match in snippet view article find links to article

Society 21:3 (2006), pp. 267–277. Parent, D. P. (1984). Exercises in Number Theory. Springer-Verlag New York. doi:10.1007/978-1-4757-5194-9. ISBN 978-1-4757-5194-9Erdős–Kac theorem (893 words) [view diff] no match in snippet view article find links to article

number theory, the Erdős–Kac theorem, named after Paul Erdős and Mark Kac, and also known as the fundamental theorem of probabilistic number theory,Partition (number theory) (4,718 words) [view diff] no match in snippet view article

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positiveCramér's conjecture (1,384 words) [view diff] no match in snippet view article find links to article

In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutiveAbstract analytic number theory (1,197 words) [view diff] no match in snippet view article find links to article

Abstract analytic number theory is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them toHermann Weyl (4,082 words) [view diff] no match in snippet view article find links to article

approximation, with his criterion for uniform distribution mod 1, which was a fundamental step in analytic number theory. This work applied to the Riemann zetaGreek letters used in mathematics, science, and engineering (3,523 words) [view diff] no match in snippet view article find links to article

longitude in astronomy the Liouville function in number theory the Carmichael function in number theory a unit of measure of volume equal to one microlitreRiemann–von Mangoldt formula (278 words) [view diff] no match in snippet view article find links to article

Bernhard Riemann and Hans Carl Friedrich von Mangoldt, describes the distribution of the zeros of the Riemann zeta function. The formula states that theUnusual number (262 words) [view diff] no match in snippet view article find links to article

In number theory, an unusual number is a natural number n whose largest prime factor is strictly greater thanCharacter sum (690 words) [view diff] no match in snippet view article find links to article

10036. Hugh L. Montgomery; Robert C. Vaughan (2007). Multiplicative number theory I. Classical theory. Cambridge tracts in advanced mathematics. 97. CambridgeSkewes's number (1,612 words) [view diff] no match in snippet view article find links to article

In number theory, Skewes's number is any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds forPrime geodesic (677 words) [view diff] no match in snippet view article find links to article

branches of mathematics, especially dynamical systems, ergodic theory, and number theory, as well as Riemann surfaces themselves. These applications often overlapHilbert's eighth problem (166 words) [view diff] no match in snippet view article find links to article

Hilbert's list of open mathematical problems posed in 1900. It concerns number theory, and in particular the Riemann hypothesis, although it is also concernedList of things named after Carl Friedrich Gauss (756 words) [view diff] no match in snippet view article find links to article

formula Gauss–Kuzmin distribution, a discrete probability distribution Gauss–Kuzmin–Wirsing constant, a constant in number theory Gauss–Manin connectionTotative (229 words) [view diff] no match in snippet view article find links to article

In number theory, a totative of a given positive integer n is an integer k such that 0 < k ≤ n and k is coprime to n. Euler's totient function φ(n) countsElliott–Halberstam conjecture (646 words) [view diff] no match in snippet view article find links to article

In number theory, the Elliott–Halberstam conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applicationsRiemann hypothesis (14,090 words) [view diff] no match in snippet view article find links to article

the Riemann zeta function—mean value theorems and the distribution of |S(T)|", J. Number Theory, 17: 93–102, doi:10.1016/0022-314X(83)90010-0 GourdonDigit sum (685 words) [view diff] no match in snippet view article find links to article

theorem, these digit sums will have a random distribution closely approximating a Gaussian distribution. The digit sum of the binary representation ofBombieri–Vinogradov theorem (484 words) [view diff] no match in snippet view article find links to article

theorem) is a major result of analytic number theory, obtained in the mid-1960s, concerning the distribution of primes in arithmetic progressions, averagedVojta's conjecture (610 words) [view diff] no match in snippet view article find links to article

analogy between diophantine approximation and Nevanlinna theory (value distribution theory) in complex analysis. It implies many other conjectures in diophantineP-adic distribution (248 words) [view diff] no match in snippet view article find links to article

In mathematics, a p-adic distribution is an analogue of ordinary distributions (i.e. generalized functions) that takes values in a ring of p-adic numbersCarmichael number (2,725 words) [view diff] no match in snippet view article find links to article

In number theory, a Carmichael number is a composite number n {\displaystyle n} which satisfies the modularBrun–Titchmarsh theorem (390 words) [view diff] no match in snippet view article find links to article

analytic number theory, the Brun–Titchmarsh theorem, named after Viggo Brun and Edward Charles Titchmarsh, is an upper bound on the distribution of primeErdős arcsine law (126 words) [view diff] no match in snippet view article find links to article

In number theory, the Erdős arcsine law, named after Paul Erdős, states that the prime divisors of a number have a distribution related to the arcsinePál Turán (1,166 words) [view diff] no match in snippet view article find links to article

probabilistic number theory". The Turán–Kubilius inequality is a generalization of this work. Turán was very interested in the distribution of primes inL-function (921 words) [view diff] no match in snippet view article find links to article

substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad generalisations of the Riemann zeta function and the L-seriesMultiplicative number theory (431 words) [view diff] no match in snippet view article find links to article

Multiplicative number theory is a subfield of analytic number theory that deals with prime numbers and with factorization and divisors. The focus is usuallyRiemann zeta function (8,424 words) [view diff] no match in snippet view article find links to article

Analytic number theory. Graduate Texts in Mathematics. 177. Springer-Verlag. Ch. 6. ISBN 0-387-98308-2. Raoh, Guo (1996). "The Distribution of the LogarithmicElliptic pseudoprime (153 words) [view diff] no match in snippet view article find links to article

In number theory, a pseudoprime is called an elliptic pseudoprime for (E, P), where E is an elliptic curve defined over the field of rational numbersPrimecoin (816 words) [view diff] no match in snippet view article find links to article

and visualization Anarchism portal Cryptography portal Economics portal Free software portal Internet portal Number theory portal Numismatics portalCyclotomic unit (358 words) [view diff] no match in snippet view article find links to article

= 1 is not of finite index in general. The cyclotomic units satisfy distribution relations. Let a be a rational number prime to p and let ga denote exp(2πia)−1SageMath (1,997 words) [view diff] no match in snippet view article find links to article

including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics. The first version of SageMath was releasedList of inequalities (679 words) [view diff] no match in snippet view article find links to article

inequality, an upper bound on the variance of any bounded probability distribution Bernstein inequalities (probability theory) Boole's inequality Borell–TISBateman–Horn conjecture (999 words) [view diff] no match in snippet view article find links to article

In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, namedGoldbach's conjecture (2,868 words) [view diff] no match in snippet view article find links to article

conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states: Every even integer greater than 2Quadratic residuosity problem (1,144 words) [view diff] no match in snippet view article find links to article

The quadratic residuosity problem in computational number theory is to decide, given integers a {\displaystyleBernhard Riemann (2,465 words) [view diff] no match in snippet view article find links to article

1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostlyList of mathematical functions (1,042 words) [view diff] no match in snippet view article find links to article

of the Gamma function useful in multivariate statistics. Student's t-distribution Elliptic integrals: Arising from the path length of ellipses; importantHarmonic number (4,856 words) [view diff] no match in snippet view article find links to article

been studied since antiquity and are important in various branches of number theory. They are sometimes loosely termed harmonic series, are closely relatedGeorge Pólya (1,619 words) [view diff] no match in snippet view article find links to article

Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for hisDirichlet's theorem on arithmetic progressions (2,765 words) [view diff] no match in snippet view article find links to article

In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, thereNumber (7,020 words) [view diff] no match in snippet view article find links to article

study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of numbers. Besides their practical usesList of things named after Peter Gustav Lejeune Dirichlet (195 words) [view diff] no match in snippet view article find links to article

Dirichlet density (number theory) Dirichlet distribution (probability theory) Dirichlet-multinomial distribution Generalized Dirichlet distribution (probabilitySerge Lang (1,917 words) [view diff] no match in snippet view article find links to article

French-born American mathematician and activist. He is known for his work in number theory and for his mathematics textbooks, including the influential AlgebraPi (17,376 words) [view diff] no match in snippet view article find links to article

sciences having little to do with the geometry of circles, such as number theory and statistics, as well as in almost all areas of physics. The ubiquityChebotarev's density theorem (2,024 words) [view diff] no match in snippet view article find links to article

Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the fieldManin conjecture (371 words) [view diff] no match in snippet view article find links to article

number theory. A tribute to Gauss and Dirichlet. Proceedings of the Gauss-Dirichlet conference, Göttingen, Germany, June 20–24, 2005. Analytic numberLists of mathematics topics (2,196 words) [view diff] no match in snippet view article find links to article

mathematicians. List of algebraic number theory topics List of number theory topics List of recreational number theory topics Glossary of arithmetic andMikio Sato (339 words) [view diff] no match in snippet view article find links to article

soliton theory, with the use of Grassmannians of infinite dimension. In number theory, he is known for the Sato–Tate conjecture on L-functions. He has beenConjecture (2,656 words) [view diff] no match in snippet view article find links to article

Riemann hypothesis is a conjecture from number theory that (amongst other things) makes predictions about the distribution of prime numbers. Few number theoristsEquidistributed sequence (2,093 words) [view diff] no match in snippet view article find links to article

is equidistributed modulo 1. This is a famous theorem of analytic number theory, published by I. M. Vinogradov in 1948. The van der Corput sequenceHarold Davenport (819 words) [view diff] no match in snippet view article find links to article

1969) was an English mathematician, known for his extensive work in number theory. Born in Huncoat, Accrington, Lancashire, he was educated at AccringtonBarban–Davenport–Halberstam theorem (347 words) [view diff] no match in snippet view article find links to article

Hildebrand, A. J.; Philipp, W. Surveys in number theory: Papers from the millennial conference on number theory. Natick, MA: A K Peters. pp. 75–108. ISBN 1-56881-162-4Effective results in number theory (863 words) [view diff] no match in snippet view article find links to article

have application to the solution of Diophantine equations, results in number theory have been scrutinised more than in other branches of mathematics toStoneham number (188 words) [view diff] no match in snippet view article find links to article

an odd prime and b is a primitive root of c2. Bugeaud, Yann (2012). Distribution modulo one and Diophantine approximation. Cambridge Tracts in MathematicsVaughan's identity (607 words) [view diff] no match in snippet view article find links to article

In mathematics and analytic number theory, Vaughan's identity is an identity found by R. C. Vaughan (1977) that can be used to simplify Vinogradov'sMellin transform (2,499 words) [view diff] no match in snippet view article find links to article

closely connected to the theory of Dirichlet series, and is often used in number theory, mathematical statistics, and the theory of asymptotic expansions; itHelge von Koch (405 words) [view diff] no match in snippet view article find links to article

Stockholm University College in 1911. Von Koch wrote several papers on number theory. One of his results was a 1901 theorem proving that the Riemann hypothesisQuadratic residue (5,542 words) [view diff] no match in snippet view article find links to article

In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integerE (mathematical constant) (4,984 words) [view diff] no match in snippet view article

{n}{\sqrt[{n}]{n!}}}} . The simplest case of a normal distribution is known as the standard normal distribution, described by this probability density function:Illegal prime (592 words) [view diff] no match in snippet view article find links to article

prime is a prime number that represents information whose possession or distribution is forbidden in some legal jurisdictions. One of the first illegal primesFiroozbakht's conjecture (666 words) [view diff] no match in snippet view article find links to article

In number theory, Firoozbakht’s conjecture (or the Firoozbakht conjecture) is a conjecture about the distribution of prime numbers. It is named after theMaier's matrix method (312 words) [view diff] no match in snippet view article find links to article

Maier's matrix method is a technique in analytic number theory due to Helmut Maier that is used to demonstrate the existence of intervals of natural numbersHans Rademacher (536 words) [view diff] no match in snippet view article find links to article

American mathematician, known for work in mathematical analysis and number theory. Rademacher received his Ph.D. in 1916 from Georg-August-UniversitätPrime-counting function (3,154 words) [view diff] no match in snippet view article find links to article

denoted by π(x) (unrelated to the number π). Of great interest in number theory is the growth rate of the prime-counting function. It was conjecturedHee Oh (549 words) [view diff] no match in snippet view article find links to article

systems. She has made contributions to dynamics and its connections to number theory. She is a student of homogeneous dynamics and has worked extensivelyGillies' conjecture (546 words) [view diff] no match in snippet view article find links to article

In number theory, Gillies' conjecture is a conjecture about the distribution of prime divisors of Mersenne numbers and was made by Donald B. Gillies inDiscrete mathematics (3,064 words) [view diff] no match in snippet view article find links to article

primality testing. Other discrete aspects of number theory include geometry of numbers. In analytic number theory, techniques from continuous mathematics areRoth's theorem (1,051 words) [view diff] no match in snippet view article find links to article

approximations. By its nature, it was ineffective (see effective results in number theory); this is of particular interest since a major application of this typeKohji Matsumoto (2,002 words) [view diff] no match in snippet view article find links to article

at Nagoya University in Nagoya, Japan. His specializations include number theory, zeta theory, and mathematical analysis. He is mostly recognized forHecke character (1,727 words) [view diff] no match in snippet view article find links to article

In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of L-functions largerEdmund Landau (575 words) [view diff] no match in snippet view article find links to article

February 1938) was a German mathematician who worked in the fields of number theory and complex analysis. Edmund Landau was born to Jewish family in BerlinChampernowne constant (1,088 words) [view diff] no match in snippet view article find links to article

certain transcendental decimal fractions by algebraic numbers, Journal of Number Theory, Volume 37, Issue 2, February 1991, Pages 231–241 Cassaigne, J.; NicolasEuler's totient function (6,126 words) [view diff] no match in snippet view article find links to article

In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using theAbc conjecture (3,748 words) [view diff] no match in snippet view article find links to article

conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory, first proposed by Joseph Oesterlé (1988) and David Masser (1985). ItEuclidean algorithm (13,979 words) [view diff] no match in snippet view article find links to article

numbers. Finally, it can be used as a basic tool for proving theorems in number theory such as Lagrange's four-square theorem and the uniqueness of prime factorizationsNormal number (4,001 words) [view diff] no match in snippet view article find links to article

Hildebrand, A.J.; Philipp, W., Surveys in number theory: Papers from the millennial conference on number theory, Natick, MA: A K Peters, pp. 57–74, ISBN 1-56881-162-4Wolfgang M. Schmidt (321 words) [view diff] no match in snippet view article find links to article

October 1933, Vienna, Austria) is a mathematician working in the area of number theory. He studied mathematics at the University of Vienna, where he receivedAkshay Venkatesh (1,044 words) [view diff] no match in snippet view article find links to article

fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodicList of mathematical theories (164 words) [view diff] no match in snippet view article find links to article

theory Morse theory Module theory Network theory Nevanlinna theory Number theory Obstruction theory Operator theory Order theory Percolation theory PerturbationList of scientific laws named after people (96 words) [view diff] no match in snippet view article find links to article

Szemerédi Euclid's theorem Number theory Euclid Euler's theorem See also: List of things named after Leonhard Euler Number theory Leonhard Euler Faraday'sMatsumoto zeta function (82 words) [view diff] no match in snippet view article find links to article

a polynomial. Matsumoto, Kohji (1990), "Value-distribution of zeta-functions", Analytic number theory ({T}okyo, 1988), Lecture Notes in Math., 1434,Perfect totient number (594 words) [view diff] no match in snippet view article find links to article

In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function toExponential sum (1,099 words) [view diff] no match in snippet view article find links to article

useful in applications. A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend startedSinkov statistic (225 words) [view diff] no match in snippet view article find links to article

Army. The mathematics involved include modular arithmetic, a bit of number theory, some linear algebra of two dimensions with matrices, some combinatoricsLogarithm (10,863 words) [view diff] no match in snippet view article find links to article

number theory and algebraic geometry, 172, Providence, RI: AMS Bookstore, p. 21, ISBN 978-0-8218-0445-2 Baker, Alan (1975), Transcendental number theoryFlorian Luca (337 words) [view diff] no match in snippet view article find links to article

mathematician who specializes in number theory with emphasis on Diophantine equations, linear recurrences and the distribution of values of arithmetic functionsWilliam J. LeVeque (591 words) [view diff] no match in snippet view article find links to article

was number theory, specifically transcendental numbers, uniform distribution, and Diophantine approximation. He wrote a number of number theory textbooksP-adic order (763 words) [view diff] no match in snippet view article find links to article

In number theory, for a given prime number p {\displaystyle p} , the pSchwartz–Bruhat function (1,548 words) [view diff] no match in snippet view article find links to article

that generalizes a Schwartz function on a real vector space. A tempered distribution is defined as a continuous linear functional on the space of Schwartz–BruhatMontgomery's pair correlation conjecture (820 words) [view diff] no match in snippet view article find links to article

(1973), "The pair correlation of zeros of the zeta function", Analytic number theory, Proc. Sympos. Pure Math., XXIV, Providence, R.I.: American MathematicalPeter Gustav Lejeune Dirichlet (3,221 words) [view diff] no match in snippet view article find links to article

mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series andNormal distribution (19,347 words) [view diff] no match in snippet view article find links to article

separate mixtures of normal distributions Erdős–Kac theorem—on the occurrence of the normal distribution in number theory Gaussian blur—convolution, whichYuri Linnik (465 words) [view diff] no match in snippet view article find links to article

January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics. Linnik was born inCubic field (1,910 words) [view diff] no match in snippet view article find links to article

In mathematics, specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three. If K is a field extensionOn the Number of Primes Less Than a Given Magnitude (610 words) [view diff] no match in snippet view article find links to article

analytic methods. Although it is the only paper Riemann ever published on number theory, it contains ideas which influenced thousands of researchers duringBig O notation (7,012 words) [view diff] no match in snippet view article find links to article

time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference betweenKaisa Matomäki (548 words) [view diff] no match in snippet view article find links to article

Matomäki (born April 30, 1985) is a Finnish mathematician specializing in number theory. Since September 2015, she has been working as an Academic ResearchDivisor summatory function (1,822 words) [view diff] no match in snippet view article find links to article

In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptoticBasel problem (2,734 words) [view diff] no match in snippet view article find links to article

Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard EulerKarl Prachar (60 words) [view diff] no match in snippet view article find links to article

mathematician who worked in the area of analytic number theory. He is known for his much acclaimed book on the distribution of the prime numbers, PrimzahlverteilungLeonhard Euler (7,071 words) [view diff] no match in snippet view article find links to article

pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology andGumbel distribution (1,488 words) [view diff] no match in snippet view article find links to article

r/(n+1) as part of the cumulative frequency analysis. In number theory, the Gumbel distribution approximates the number of terms in a random partition ofRegular prime (3,179 words) [view diff] no match in snippet view article find links to article

In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem.Refactorable number (515 words) [view diff] no match in snippet view article find links to article

and judges definitions from a variety of areas of mathematics such as number theory and graph theory. Colton called such numbers "refactorable". While computerThree-gap theorem (1,344 words) [view diff] no match in snippet view article find links to article

Press, ISBN 0-521-81220-8, Zbl 1001.68093 Sós, V. T. (1958), "On the distribution mod 1 of the sequence n αLiouville function (627 words) [view diff] no match in snippet view article find links to article

λ(n) and named after Joseph Liouville, is an important function in number theory. If n is a positive integer, then λ(n) is defined as:Haar measure (4,308 words) [view diff] no match in snippet view article find links to article

"invariant integral". Haar measures are used in many parts of analysis, number theory, group theory, representation theory, statistics, probability theoryTimeline of number theory (718 words) [view diff] no match in snippet view article find links to article

A timeline of number theory. ca. 20,000 BC — Nile Valley, Ishango Bone: possibly the earliest reference to prime numbers and Egyptian multiplicationChebyshev's bias (439 words) [view diff] no match in snippet view article find links to article

In number theory, Chebyshev's bias is the phenomenon that most of the time, there are more primes of the form 4k + 3 than of the form 4k + 1, up to theMaier's theorem (358 words) [view diff] no match in snippet view article find links to article

In number theory, Maier's theorem (Maier 1985) is a theorem about the numbers of primes in short intervals for which Cramér's probabilistic model of primesRamin Takloo-Bighash (176 words) [view diff] no match in snippet view article find links to article

the distribution of rational points on certain group compactifications. He is a co-author, with Steven J. Miller, of An Invitation To Modern Number TheoryGlossary of areas of mathematics (6,381 words) [view diff] no match in snippet view article find links to article

algebra. Abstract analytic number theory: a branch of mathematics that takes ideas from classical analytic number theory and applies them to variousMertens conjecture (1,213 words) [view diff] no match in snippet view article find links to article

large amount of computational evidence in favor of a conjecture. In number theory, we define the Mertens function as MNumber Theory: An Approach through History from Hammurapi to Legendre (195 words) [view diff] no match in snippet view article find links to article

Number Theory, An Approach through History from Hammurapi to Legendre is a book on the history of number theory, written by André Weil. The book reviewsCarl Friedrich Gauss (7,666 words) [view diff] no match in snippet view article find links to article

mathematician who made significant contributions to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysicsPierre François Verhulst (471 words) [view diff] no match in snippet view article find links to article

Brussels – 15 February 1849, Brussels) was a mathematician and a doctor in number theory from the University of Ghent in 1825. Verhulst published in 1838 theGamma function (9,751 words) [view diff] no match in snippet view article find links to article

Given Quantity"), one of the milestones in the development of analytic number theory—the branch of mathematics that studies prime numbers using the toolsFerdinand Georg Frobenius (1,436 words) [view diff] no match in snippet view article find links to article

contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famous determinantal identitiesElementary proof (613 words) [view diff] no match in snippet view article find links to article

only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some timeVon Mangoldt function (1,370 words) [view diff] no match in snippet view article find links to article

Tenenbaum (1995) p.30 Apostol (1976) p.33 Schroeder, Manfred R. (1997). Number theory in science and communication. With applications in cryptography, physicsHelmut Maier (513 words) [view diff] no match in snippet view article find links to article

University of Ulm, Germany. He is known for his contributions in analytic number theory and mathematical analysis and particularly for the so-called Maier'sPractical number (2,748 words) [view diff] no match in snippet view article find links to article

In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sumsHua Luogeng (1,674 words) [view diff] no match in snippet view article find links to article

was a Chinese mathematician famous for his important contributions to number theory and for his role as the leader of mathematics research and educationGraham Everest (283 words) [view diff] no match in snippet view article find links to article

fields were the interaction of dynamical systems and number theory and recursive equations in number theory. In 1983 he became a member of the London MathematicalHeath-Brown–Moroz constant (188 words) [view diff] no match in snippet view article find links to article

the primes. This constant is part of an asymptotic estimate for the distribution of rational points of bounded height on the cubic surface X03=X1X2X3Adrien-Marie Legendre (1,681 words) [view diff] no match in snippet view article find links to article

He also did pioneering work on the distribution of primes, and on the application of analysis to number theory. His 1798 conjecture of the prime numberTibor Šalát (455 words) [view diff] no match in snippet view article find links to article

professor of mathematics, and Doctor of Mathematics who specialized in number theory and real analysis. He was the author and co-author of undergraduateElliptic unit (423 words) [view diff] no match in snippet view article find links to article

prime p then Θa(Q) is a unit away from p. The function Θa satisfies a distribution relation for b = (β) coprime to a:Phi (1,163 words) [view diff] no match in snippet view article find links to article

mathematics, art, and architecture. Euler's totient function φ(n) in number theory; also called Euler's phi function. The cyclotomic polynomial functionsLegendre's constant (562 words) [view diff] no match in snippet view article find links to article

Poussin, C. Mém. Couronnés Acad. Roy. Belgique 59, 1-74, 1899 Sur la distribution des zéros de la fonction ζ (Timothy Browning (233 words) [view diff] no match in snippet view article find links to article

contributions on the interface of analytic number theory and arithmetic geometry concerning the number and distribution of rational and integral solutions toPan Chengdong (261 words) [view diff] no match in snippet view article find links to article

1997) was a Chinese mathematician who made numerous contributions to number theory, including the Goldbach's conjecture. He was vice president of ShandongNick Katz (620 words) [view diff] no match in snippet view article find links to article

particularly on p-adic methods, monodromy and moduli problems, and number theory. He is currently a professor in the Mathematics Department at PrincetonHarald Cramér (1,080 words) [view diff] no match in snippet view article find links to article

was highly involved in analytic number theory. He also made some important statistical contributions to the distribution of primes and twin primes. HisComplex number (11,279 words) [view diff] no match in snippet view article find links to article

Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem forIstván Vincze (mathematician) (623 words) [view diff] no match in snippet view article

mathematician, known for his contributions to number theory, non-parametric statistics, empirical distribution, Cramér–Rao inequality, and information theoryVera T. Sós (804 words) [view diff] no match in snippet view article find links to article

(born September 11, 1930) is a Hungarian mathematician, specializing in number theory and combinatorics. She was a student and close collaborator of bothPoisson summation formula (2,918 words) [view diff] no match in snippet view article find links to article

0 {\displaystyle f=0} (Pinsky 2002). In number theory, Poisson summation can also be used to derive a variety of functionalMark Pollicott (206 words) [view diff] no match in snippet view article find links to article

in applications to other areas of mathematics, including geometry, number theory and analysis. Pollicott attended High Pavement College in NottinghamList of important publications in mathematics (9,468 words) [view diff] no match in snippet view article find links to article

Dedekind Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P. G. Lejeune DirichletRobert Alexander Rankin (603 words) [view diff] no match in snippet view article find links to article

27 January 2001) was a Scottish mathematician who worked in analytic number theory. Rankin was born in Garlieston in Wigtownshire the son of Rev OliverGaussian integer (4,772 words) [view diff] no match in snippet view article find links to article

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary additionPaul Vojta (202 words) [view diff] no match in snippet view article find links to article

September 30, 1957) is an American mathematician, known for his work in number theory on diophantine geometry and diophantine approximation. In formulatingHilbert–Pólya conjecture (1,403 words) [view diff] no match in snippet view article find links to article

(1973). David Hilbert did not work in the central areas of analytic number theory, but his name has become known for the Hilbert–Pólya conjecture forOhio State University Press (127 words) [view diff] no match in snippet view article find links to article

reviewed by national media in 2017. "Publishers served by the Chicago Distribution Center". University of Chicago Press. Retrieved 2017-09-12. "New directorPaul T. Bateman (598 words) [view diff] no match in snippet view article find links to article

of Analytic Number Theory: An Introductory Course. He was also a contributor to the second edition of the textbook Elementary Number Theory, a translationKlaus Roth (376 words) [view diff] no match in snippet view article find links to article

Schmidt, W. M.; Vaughan, R. C., eds. (2009), "Klaus Roth at 80", Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthdayEuler–Mascheroni constant (4,277 words) [view diff] no match in snippet view article find links to article

Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ). It is definedAsymptotic analysis (2,310 words) [view diff] no match in snippet view article find links to article

Asymptote Asymptotic computational complexity Asymptotic density (in number theory) Asymptotic theory (statistics) Asymptotology Big O notation Leading-orderTranscendental number (4,880 words) [view diff] no match in snippet view article find links to article

"Number theory and formal languages". In Hejhal, Dennis A.; Friedman, Joel; Gutzwiller, Martin C.; Odlyzko, Andrew M. Emerging applications of numberPéter Kiss (mathematician) (598 words) [view diff] no match in snippet view article

professor of mathematics at Eszterházy Károly College, who specialized in number theory. In 1992 he won the Albert Szent-Györgyi Prize for his achievementsSolomon W. Golomb (847 words) [view diff] no match in snippet view article find links to article

pentominoes in 1953. He specialized in problems of combinatorial analysis, number theory, coding theory, and communications. His game of pentomino inspired TetrisRodion Kuzmin (449 words) [view diff] no match in snippet view article find links to article

1949, Leningrad) was a Russian mathematician, known for his works in number theory and analysis. His name is sometimes transliterated as Kusmin. He wasJonas Kubilius (1,130 words) [view diff] no match in snippet view article find links to article

was a Lithuanian mathematician who worked in probability theory and number theory. He was rector of Vilnius University for 32 years, and served one termPrime gap (2,934 words) [view diff] no match in snippet view article find links to article

Pintz, J. (1997). "Very large gaps between consecutive primes". J. Number Theory. 63 (2): 286–301. doi:10.1006/jnth.1997.2081. Erdős, Some of my favouriteIlya Piatetski-Shapiro (2,144 words) [view diff] no match in snippet view article find links to article

years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contributionElectrical network (1,121 words) [view diff] no match in snippet view article find links to article

circuit. Simple linear circuits can be analyzed by hand using complex number theory. In more complex cases the circuit may be analyzed with specializedList of mathematical symbols (1,288 words) [view diff] no match in snippet view article find links to article

comparison is of smaller order than, is of greater order than analytic number theory f ≪ g means the growth of f is asymptotically bounded by g. (ThisComputational hardness assumption (3,127 words) [view diff] no match in snippet view article find links to article

that a specific problem is hard on most instances from some explicit distribution, whereas a worst-case assumption only says that the problem is hard onProblems involving arithmetic progressions (569 words) [view diff] no match in snippet view article find links to article

Problems involving arithmetic progressions are of interest in number theory, combinatorics, and computer science, both from theoretical and applied pointsBernoulli number (11,790 words) [view diff] no match in snippet view article find links to article

numbers Bn are a sequence of rational numbers which occur frequently in number theory. The values of the first 20 Bernoulli numbers are given in the tableProbabilistic method (1,604 words) [view diff] no match in snippet view article find links to article

This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (eStatistics (7,510 words) [view diff] no match in snippet view article find links to article

essential methodology in certain areas. In number theory, scatter plots of data generated by a distribution function may be transformed with familiar toolsChange-making problem (1,379 words) [view diff] no match in snippet view article find links to article

where uncertainty or fuzziness in the goal amount W makes it a discrete distribution rather than a fixed quantity, where the value of each coin is likewiseOutline of arithmetic (221 words) [view diff] no match in snippet view article find links to article

Percentage Permutations Proportion Rounding Scientific notation Outline of number theory Riemann zeta function L-functions Multiplicative functions Modular formsFermat pseudoprime (1,894 words) [view diff] no match in snippet view article find links to article

In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Fermat's little theoremUnit fraction (1,051 words) [view diff] no match in snippet view article find links to article

representations. The topic of Egyptian fractions has also seen interest in modern number theory; for instance, the Erdős–Graham conjecture and the Erdős–Straus conjectureJacques Hadamard (1,819 words) [view diff] no match in snippet view article find links to article

October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differentialVinogradov's theorem (999 words) [view diff] no match in snippet view article find links to article

In number theory, Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbersLaplace–Stieltjes transform (1,347 words) [view diff] no match in snippet view article find links to article

ISBN 0-201-00288-4. Apostol, T.M. (1997), Modular Functions and Dirichlet Series in Number Theory (2nd ed.), New York: Springer-Verlag, ISBN 0-387-97127-0 . GrimmettUlam spiral (2,176 words) [view diff] no match in snippet view article find links to article

Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial hasRamanujan's congruences (984 words) [view diff] no match in snippet view article find links to article

Mathematics. 15: 341. doi:10.1112/S1461157012001088. Ono, Ken (2000). "Distribution of the partition function modulo m". Annals of Mathematics. Second SeriesFields Medal (2,841 words) [view diff] no match in snippet view article find links to article

fields. His work did much to unify algebraic geometry and algebraic number theory." Charles Fefferman Princeton University, US Princeton UniversityBeurling zeta function (225 words) [view diff] no match in snippet view article find links to article

need not hold. Abstract analytic number theory Bateman, Paul T.; Diamond, Harold G. (1969), "Asymptotic distribution of Beurling's generalized primeWhite South Africans (5,631 words) [view diff] no match in snippet view article find links to article

professor of mathematics, specialising in number theory Stanley Skewes, mathematician whose work in number theory produced the record breaking Skewes numberContributions of Leonhard Euler to mathematics (2,108 words) [view diff] no match in snippet view article find links to article

solve number theory problems. In doing so, he united two disparate branches of mathematics and introduced a new field of study, analytic number theory. InTwin prime (2,182 words) [view diff] no match in snippet view article find links to article

infinitely many twin primes has been one of the great open questions in number theory for many years. This is the content of the twin prime conjecture, whichSylvester Medal (499 words) [view diff] no match in snippet view article find links to article

Wirtinger Austrian Wirtinger worked on complex analysis, geometry, algebra, number theory, Lie groups and knot theory; he was honored for his work on the generalZeta function regularization (2,144 words) [view diff] no match in snippet view article find links to article

attempts to give precise meanings to ill-conditioned sums appearing in number theory. There are several different summation methods called zeta functionGlossary of arithmetic and diophantine geometry (4,885 words) [view diff] no match in snippet view article find links to article

traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposedHarald Niederreiter (696 words) [view diff] no match in snippet view article find links to article

Number Theory, retrieved 2015-07-18. Larcher, Gerhard; Pillichshammer, Friedrich; Winterhof, Arne; et al., eds. (2014), Applied Algebra and Number Theory:Latin letters used in mathematics (2,396 words) [view diff] no match in snippet view article find links to article

in Hamiltonian mechanics h represents: the class number in algebraic number theory a small increment in the argument of a function the unit hour for timeRSA (cryptosystem) (7,579 words) [view diff] no match in snippet view article

1976. They also introduced digital signatures and attempted to apply number theory. Their formulation used a shared-secret-key created from exponentiationOutline of science (8,762 words) [view diff] no match in snippet view article find links to article

triangles Number theory – branch of pure mathematics devoted primarily to the study of the integers Analytic number theory – branch of number theory that usesS.I.N. Theory (835 words) [view diff] no match in snippet view article find links to article

S.I.N. Theory (abbreviation for Social Insurance Number Theory) is a 2012 Canadian science fiction drama film about a mathematics professor creating anGlossary of artificial intelligence (1,175 words) [view diff] no match in snippet view article find links to article

role. Computational neuroscience – Computational number theory – also known as algorithmic number theory, it is the study of algorithms for performing numberCousin prime (516 words) [view diff] no match in snippet view article find links to article

ISBN 1118045718. Fine, Benjamin; Rosenberger, Gerhard (2007). Number theory: an introduction via the distribution of primes. Birkhäuser. p. 206. ISBN 0817644725.Fourier transform (16,932 words) [view diff] no match in snippet view article find links to article

properties. The formula has applications in engineering, physics, and number theory. The frequency-domain dual of the standard Poisson summation formulaWilliam Duke (mathematician) (435 words) [view diff] no match in snippet view article

Drexel Duke (born 1958) is an American mathematician specializing in number theory. Duke studied at the University of New Mexico and then at New York UniversityTheorem (3,580 words) [view diff] no match in snippet view article find links to article

Theorem, and there are many other examples of simple yet deep theorems in number theory and combinatorics, among other areas. Other theorems have a known proofKhinchin's constant (1,335 words) [view diff] no match in snippet view article find links to article

In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, coefficients ai of the continued fraction expansion of x haveRichard Garfield (1,298 words) [view diff] no match in snippet view article find links to article

Wilf, Herbert S (1 May 1992). "The distribution of the binomial coefficients modulo p". Journal of Number Theory. 41 (1): 1–5. doi:10.1016/0022-314X(92)90078-4Alexandru Froda (649 words) [view diff] no match in snippet view article find links to article

important contributions in the field of mathematical analysis, algebra, number theory and rational mechanics. In his 1929 thesis he proved what is now knownGiuseppe Melfi (434 words) [view diff] no match in snippet view article find links to article

{\displaystyle n} . Among other problems in elementary number theory, he is the author of a theorem that allowed him to get a 5328-digitNevanlinna theory (2,597 words) [view diff] no match in snippet view article find links to article

events of (the twentieth) century." The theory describes the asymptotic distribution of solutions of the equation ƒ(z) = a, as a varies. A fundamental toolGérald Tenenbaum (416 words) [view diff] no match in snippet view article find links to article

probabilistic number theory, Gérald Tenenbaum received the A-X Gaston Julia prize in 1976, the Albert Châtelet medal in algebra and number theory in 1985 andErgodic theory (3,515 words) [view diff] no match in snippet view article find links to article

Lie theory (representation theory, lattices in algebraic groups), and number theory (the theory of diophantine approximations, L-functions). ErgodicRule 90 (3,239 words) [view diff] no match in snippet view article find links to article

problem in number theory, Gilbreath's conjecture, on the differences of consecutive prime numbers. This rule is also connected to number theory in a differentBell number (3,922 words) [view diff] no match in snippet view article find links to article

interpretation, as moments of probability distributions. In particular, Bn is the nth moment of a Poisson distribution with mean 1. In generalHenri Poincaré (8,864 words) [view diff] no match in snippet view article find links to article

by Grigori Perelman. Poincaré recurrence theorem hyperbolic geometry number theory the three-body problem the theory of diophantine equations the theoryAugustin-Louis Cauchy (5,539 words) [view diff] no match in snippet view article find links to article

Cauchy's convergence test Cauchy (crater) Cauchy determinant Cauchy distribution Cauchy's equation Cauchy–Euler equation Cauchy functional equation CauchyPublic-key cryptography (7,100 words) [view diff] no match in snippet view article find links to article

(2008-05-01). "Protecting communications against forgery" (PDF). Algorithmic Number Theory. MSRI Publications. 44. §5: Public-key signatures, pp. 543–545. Retrieved1935 in science (1,381 words) [view diff] no match in snippet view article find links to article

Alonzo Church presents his paper "An unsolvable problem of elementary number theory", introducing his theorem on the Entscheidungsproblem, to the AmericanMertens function (1,445 words) [view diff] no match in snippet view article find links to article

In number theory, the Mertens function is defined for all positive integers n as M ( n ) =Hale Trotter (501 words) [view diff] no match in snippet view article find links to article

among other topics, probability theory, group theory computations, number theory, and knot theory. In 1963 he solved an open problem in knot theory byHurwitz zeta function (3,070 words) [view diff] no match in snippet view article find links to article

function occurs in a variety of disciplines. Most commonly, it occurs in number theory, where its theory is the deepest and most developed. However, it alsoAlmost surely (1,243 words) [view diff] no match in snippet view article find links to article

{\displaystyle {\tfrac {(1+\epsilon )\ln n}{n}}} for any ε > 0. In number theory this is referred to as "almost all", as in "almost all numbers are composite"Liouville number (3,357 words) [view diff] no match in snippet view article find links to article

In number theory, a Liouville number is an irrational number x with the property that, for every positive integer n, there exist integers p and q withPythagorean triple (9,768 words) [view diff] no match in snippet view article find links to article

originally proved by Fermat, see Koshy, Thomas (2002), Elementary Number Theory with Applications, Academic Press, p. 545, ISBN 9780124211711 . ForKummer sum (741 words) [view diff] no match in snippet view article find links to article

automorphic forms for the metaplectic group, and Vaughan's lemma in analytic number theory. A second conjecture on Kummer sums was made by J. W. S. Cassels, againElliptic curve primality (4,672 words) [view diff] no match in snippet view article find links to article

Lawrence C., Elliptic Curves: Number Theory and Cryptography, Chapman & Hall/CRC, 2003 Koblitz, Neal, Introduction to Number Theory and Cryptography, 2nd EdHistory of mathematics (14,201 words) [view diff] no match in snippet view article find links to article

simplistic understandings of both the Sieve of Eratosthenes and perfect number theory (namely, that of the number 6). It also shows how to solve first orderWallenius' noncentral hypergeometric distribution (1,875 words) [view diff] no match in snippet view article find links to article

A. (2007). "Random number theory". Fog, A. (2008). "Calculation Methods for Wallenius' Noncentral Hypergeometric Distribution". Communications in staticticsFrench mathematical seminars (309 words) [view diff] no match in snippet view article find links to article

1950s Séminaire Delange-Pisot, then Delange-Pisot-Poitou, from 1959[2], number theory Séminaire Ehresmann, differential geometry and category theory; CharlesLambda (1,396 words) [view diff] no match in snippet view article find links to article

the city itself. Lambda is the von Mangoldt function in mathematical number theory. In statistics, Wilks's lambda is used in multivariate analysis of varianceArs Conjectandi (3,909 words) [view diff] no match in snippet view article find links to article

motivation and applications of a sequence of numbers more closely related to number theory than probability; these Bernoulli numbers bear his name today, and are1837 in science (811 words) [view diff] no match in snippet view article find links to article

tackle an algebraic problem and thus creating the branch of analytic number theory. In proving the theorem, he introduces the Dirichlet characters andSigma (1,022 words) [view diff] no match in snippet view article find links to article

{\displaystyle \sigma (A)} the sum-of-divisors function in number theory the Stefan–Boltzmann constant the "sigma factor" of RNA polymerase aNoncentral hypergeometric distributions (2,341 words) [view diff] no match in snippet view article find links to article

Agner (2007), Random number theory . Fog, Agner (2008), "Calculation Methods for Wallenius' Noncentral Hypergeometric Distribution", Communications inList of mathematical proofs (586 words) [view diff] no match in snippet view article find links to article

(graph theory) Lagrange's theorem (group theory) Lagrange's theorem (number theory) Liouville's theorem (complex analysis) Markov's inequality (proof ofMichał Kalecki (6,752 words) [view diff] no match in snippet view article find links to article

and generalized Pascal's theorem. His investigations now centered on number theory and probability. Kalecki's engagement in mathematics helped him to relieveFisher's noncentral hypergeometric distribution (2,348 words) [view diff] no match in snippet view article find links to article

hypergeometric distribution", Statistica Neerlandica, 65 (1), pp. 22–31, doi:10.1111/j.1467-9574.2010.00468.x . Fog, A. (2007), Random number theory . Fog, AFelix Klein Protocols (128 words) [view diff] no match in snippet view article find links to article

surface. 8 1886–1887 9 1887–1889 10 1889–1892 11 1892–1894 Number theory. (distribution of primes; Diophantus and his works, quadratic and biquadraticIdeal lattice cryptography (5,743 words) [view diff] no match in snippet view article find links to article

of cyclic lattices. Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular, they have a significant placeD. R. Kaprekar (995 words) [view diff] no match in snippet view article find links to article

done on Harshad numbers, and their distribution, frequency, etc. are a matter of considerable interest in number theory today. Kaprekar also studied thePartition problem (2,272 words) [view diff] no match in snippet view article find links to article

In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integersErdős–Turán inequality (444 words) [view diff] no match in snippet view article find links to article

uniform distribution. II". Nederl. Akad. Wetensch. 51: 1262–1269. MR 0027895. Zbl 0032.01601. Harman, Glyn (1998). Metric Number Theory. London MathematicalMillennium Prize Problems (1,173 words) [view diff] no match in snippet view article find links to article

disproof of this would have far-reaching implications in number theory, especially for the distribution of prime numbers. This was Hilbert's eighth problemCryptography (8,622 words) [view diff] no match in snippet view article find links to article

computational complexity, statistics, combinatorics, abstract algebra, number theory, and finite mathematics generally. Cryptography is also a branch ofFreeman Dyson (7,898 words) [view diff] no match in snippet view article find links to article

resigned his professorship in 1947. In 1947, Dyson published two papers in number theory. Friends and colleagues describe him as shy and self-effacing, withGolden ratio (10,176 words) [view diff] no match in snippet view article find links to article

Retrieved 30 May 2006. James Joseph Tattersall (2005). Elementary number theory in nine chapters (2nd ed.). Cambridge University Press. p. 28. ISBN 978-0-521-85014-8The Art of Computer Programming (2,876 words) [view diff] no match in snippet view article find links to article

Logarithms 1.2.3. Sums and Products 1.2.4. Integer Functions and Elementary Number Theory 1.2.5. Permutations and Factorials 1.2.6. Binomial Coefficients 1.2Hà Huy Khoái (807 words) [view diff] no match in snippet view article find links to article

for p-adic meromorphic functions, J. Number Theory, 87(2001), 211-221 (with Ta Thi Hoai An) . Value Distribution for p-adic hypersurfaces, Taiwanese JBc (programming language) (1,681 words) [view diff] no match in snippet view article

contains functions of trigonometry, exponential functions, functions of number theory and some mathematical constants scientific_constants.bc - contains particleCarl-Gustav Esseen (477 words) [view diff] no match in snippet view article find links to article

telecommunications. After retirement, Esseen worked on topics from number theory, especially factorization, a topic of importance in cryptology. EsseenAlexei Venkov (675 words) [view diff] no match in snippet view article find links to article

the spectral theory of automorphic forms and their applications in number theory and mathematical physics. He has proved partial results for the Roelcke-SelbergPolylogarithm (9,123 words) [view diff] no match in snippet view article find links to article

Zagier, D. (1989). "The dilogarithm function in geometry and number theory". Number Theory and Related Topics: papers presented at the Ramanujan ColloquiumNumber sign (3,690 words) [view diff] no match in snippet view article find links to article

connected sum of manifolds A and B, or of knots A and B in knot theory. In number theory, n# is the primorial of n. In many scripting languages and data fileMathematics Subject Classification (1,340 words) [view diff] no match in snippet view article find links to article

05: Combinatorics 06: Order theory 08: General algebraic systems 11: Number theory 12: Field theory and polynomials 13: Commutative rings and algebrasQuantum Bayesianism (7,615 words) [view diff] no match in snippet view article find links to article

Steven; McConnell, Gary; Yard, Jon (2017-04-24). "SICs and Algebraic Number Theory". Foundations of Physics. 47: 1–18. arXiv:1701.05200 . Bibcode:2017FoPhHardy–Littlewood tauberian theorem (1,206 words) [view diff] no match in snippet view article find links to article

ISBN 978-0-8218-2023-0. Narkiewicz, Władysław (2000). The Development of Prime Number Theory. Berlin: Springer-Verlag. ISBN 3-540-66289-8. Hazewinkel, MichielClosed-form expression (1,356 words) [view diff] no match in snippet view article find links to article

transcendental numbers. Closed-form numbers can be studied via transcendental number theory, in which a major result is the Gelfond–Schneider theorem, and a majorMaple (software) (2,242 words) [view diff] no match in snippet view article

linear and non-linear control systems Discrete math tools including number theory Tools for visualizing and analysing directed and undirected graphs GroupFeedback with Carry Shift Registers (1,058 words) [view diff] no match in snippet view article find links to article

generalizing work of Marsaglia and Zaman. FCSRs are analyzed using number theory. Associated with the FCSR is a connection integerComplexity function (1,303 words) [view diff] no match in snippet view article find links to article

Berthé, Valérie; Rigo, Michel, eds. (2010). Combinatorics, automata, and number theory. Encyclopedia of Mathematics and its Applications. 135. Cambridge: CambridgeGeneralized function (2,180 words) [view diff] no match in snippet view article find links to article

in number theory, particularly to adelic algebraic groups. André Weil rewrote Tate's thesis in this language, characterizing the zeta distribution onMiller–Rabin primality test (3,322 words) [view diff] no match in snippet view article find links to article

(1980), "Probabilistic algorithm for testing primality", Journal of Number Theory, 12 (1): 128–138, doi:10.1016/0022-314X(80)90084-0 F. Arnault (AugustIndicator function (2,076 words) [view diff] no match in snippet view article find links to article

generalization of the inverse of the indicator function in elementary number theory, the Möbius function. (See paragraph below about the use of the inverseAlexander Grothendieck (6,597 words) [view diff] no match in snippet view article find links to article

the IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory and complex analysis. His first (pre-IHÉS)Kolakoski sequence (3,080 words) [view diff] no match in snippet view article find links to article

Lagarias, J. C. (1992). "Number Theory and Dynamical Systems". In Burr, S. A. The Unreasonable Effectiveness of Number Theory. Providence, RI: AmericanGeneralized Riemann hypothesis (1,308 words) [view diff] no match in snippet view article find links to article

Algebraic Number Fields: 409–464. Davenport, Harold. Multiplicative number theory. Third edition. Revised and with a preface by Hugh L. Montgomery. GraduateNaor–Reingold pseudorandom function (1,957 words) [view diff] no match in snippet view article find links to article

"ANTS-III: Proceedings of the Third International Symposium on Algorithmic Number Theory,1998,48–63. Shparlinski, Igor E. "Linear Complexity of the Naor–ReingoldDifferential equation (3,769 words) [view diff] no match in snippet view article find links to article

Category theory Control theory Graph theory Computation Algebra Number theory Elementary Linear Multilinear Abstract Combinatorics Group theoryErdős–Bacon number (4,071 words) [view diff] no match in snippet view article find links to article

Noga; Erdös, P. (1985). "An Application of Graph Theory to Additive Number Theory". European Journal of Combinatorics. 6 (3): 201–3. doi:10.1016/S0195-6698(85)80027-5Thue–Morse sequence (3,125 words) [view diff] no match in snippet view article find links to article

sequence was first studied by Eugène Prouhet in 1851, who applied it to number theory. However, Prouhet did not mention the sequence explicitly; this wasIreland (18,569 words) [view diff] no match in snippet view article find links to article

inspired Adam Smith, among others. John B. Cosgrave was a specialist in number theory and discovered a 2000-digit prime number in 1999 and a record compositeMathematical challenges (206 words) [view diff] no match in snippet view article find links to article

disproof of this would have far-reaching implications in number theory, especially for the distribution of prime numbers. There are several professional organizationsJohn McKay (mathematician) (2,218 words) [view diff] no match in snippet view article

J. (1979). "Polynomials with PSL(2,7) as Galois group". Journal of Number Theory. 11 (1): 69–75. doi:10.1016/0022-314X(79)90020-9. MR 0527761. McKayQuaternion (10,512 words) [view diff] no match in snippet view article find links to article

terms of quaternions. Quaternions have received another boost from number theory because of their relationships with the quadratic forms. Since 1989Edgar Gilbert (1,703 words) [view diff] no match in snippet view article find links to article

colossal book of mathematics: classic puzzles, paradoxes, and problems : number theory, algebra, geometry, probability, topology, game theory, infinity, andTaylor's law (13,787 words) [view diff] no match in snippet view article find links to article

flow heterogeneity the genomic distributions of single-nucleotide polymorphisms (SNPs) gene structures in number theory with sequential values of the MertensRiesz mean (745 words) [view diff] no match in snippet view article find links to article

an inverse Mellin transform. Another interesting case connected with number theory arises by taking aList of victims of Nazism (206 words) [view diff] no match in snippet view article find links to article

leader executed by firing squad Otto Blumenthal 1876–1944 German Work in number theory, editor of Mathematische Annalen Theresienstadt Felix Hausdorff 1868–1942Arithmetic Fuchsian group (3,797 words) [view diff] no match in snippet view article find links to article

Peter (1982). "Class numbers of indefinite binary quadratic forms". J. Number Theory. 15: 229–247. doi:10.1016/0022-314x(82)90028-2. Katz, M.; Schaps,Jean-Marie De Koninck (1,750 words) [view diff] no match in snippet view article find links to article

l'ingénieur, Éditions Loze, Montréal, 2004 1001 Problems in Classical Number Theory (with Armel Mercier), American Mathematical Society, 2007 Ces nombresVector space (11,578 words) [view diff] no match in snippet view article find links to article

of examples of vector spaces, particularly in algebra and algebraic number theory: a field F containing a smaller field E is an E-vector space, by theWu Chinese-speaking people (2,628 words) [view diff] no match in snippet view article find links to article

Hua Luogeng (1910–1985), famous for his important contributions to number theory and for his role as the leader of mathematics research and educationList of scientific equations named after people (330 words) [view diff] no match in snippet view article find links to article

Arrhenius equation Chemical kinetics Svante Arrhenius Aryabhata equation Number theory Aryabhata Ashkin–Teller model Statistical mechanics Edward Teller JuliusChebyshev function (2,129 words) [view diff] no match in snippet view article find links to article

Theory of the Distribution of Primes", Acta Mathematica, 41 (1916) pp. 119–196. ^ Davenport, Harold (2000). In Multiplicative Number Theory. Springer. pRoyal Medal (350 words) [view diff] no match in snippet view article find links to article

recognition of his achievements in number theory, in particular Fermats Last Theorem and his achievements in algebraic number theory particularly the celebratedFourier analysis (4,072 words) [view diff] no match in snippet view article find links to article

scientific applications – in physics, partial differential equations, number theory, combinatorics, signal processing, digital image processing, probabilityJohn von Neumann (16,179 words) [view diff] no match in snippet view article find links to article

But as for mathematics, he contributed to every part of it except number theory and topology. That is, I think, something unique."Von Neumann was askedSPECfp (705 words) [view diff] no match in snippet view article find links to article

protein-inhibitor complex which is embedded in water. 189.lucas Fortran 90 Number Theory / Primality Testing Computes the Lucas-Lehmer test to check primalityFeynman–Kac formula (1,959 words) [view diff] no match in snippet view article find links to article

Baclawski, K.; Donsker, M. D., eds. (1979). Mark Kac: Probability, Number Theory, and Statistical Physics, Selected Papers. Cambridge, Massachusetts:Volkenborn integral (610 words) [view diff] no match in snippet view article find links to article

p-adisches Integral und seine Anwendungen II. In: Manuscripta Mathematica. Bd. 12, Nr. 1, 1974, [2] Henri Cohen, "Number Theory", Volume II, page 276Binomial coefficient (10,647 words) [view diff] no match in snippet view article find links to article

least common multiple of some finite sequence of integers. Journal of Number Theory 125 (2007), 393-411. doi:10.1016/j.jnt.2006.10.017 Farhi, Bakir. NontrivialTimeline of mathematics (7,034 words) [view diff] no match in snippet view article find links to article

formula. 1801 – Disquisitiones Arithmeticae, Carl Friedrich Gauss's number theory treatise, is published in Latin. 1805 – Adrien-Marie Legendre introducesCounter-Earth (2,340 words) [view diff] no match in snippet view article find links to article

believes Aristotle was having a joke "at the expense of Pythagorean number theory", and that the true purpose of the Counter-Earth was to "balance" Philolaus'Expander graph (2,684 words) [view diff] no match in snippet view article find links to article

Davidoff, Guiliana; Sarnak, Peter; Valette, Alain (2003), Elementary number theory, group theory and Ramanujan graphs, LMS student texts, 55, CambridgeÉmile Borel (987 words) [view diff] no match in snippet view article find links to article

theory of functions (PhD thesis, 1894) Introduction to the study of number theory and superior algebra (1895) A course on the theory of functions (1898)Fast Fourier transform (6,773 words) [view diff] no match in snippet view article find links to article

theories, from simple complex-number arithmetic to group theory and number theory; this article gives an overview of the available techniques and someMatrix (mathematics) (12,135 words) [view diff] no match in snippet view article

probability distributions, such as matrix normal distribution. Beyond probability theory, they are applied in domains ranging from number theory to physicsList of eponymous laws (8,198 words) [view diff] no match in snippet view article find links to article

Named for Archimedes. Artin reciprocity law is a general theorem in number theory that forms a central part of global class field theory. Named afterGovernment Communications Headquarters (6,764 words) [view diff] no match in snippet view article find links to article

for CESG (and before it, CESD) since 1965. Ellis lacked the necessary number theory expertise necessary to build a workable system. Subsequently, a feasibleBinary logarithm (4,794 words) [view diff] no match in snippet view article find links to article

than the binary logarithm in many areas of pure mathematics such as number theory and mathematical analysis, the binary logarithm has several applicationsFibonacci word (1,701 words) [view diff] no match in snippet view article find links to article

approximation", in Berthé, Valérie; Rigo, Michael, Combinatorics, automata, and number theory, Encyclopedia of Mathematics and its Applications, 135, Cambridge: CambridgeDiffie–Hellman problem (846 words) [view diff] no match in snippet view article find links to article

ANTS-III: Proceedings of the Third International Symposium on Algorithmic Number Theory. Springer-Verlag: 48–63. doi:10.1007/bfb0054851. Retrieved 2005-11-23Continued fraction (7,566 words) [view diff] no match in snippet view article find links to article

ISBN 0-486-69630-8. Long, Calvin T. (1972), Elementary Introduction to Number Theory (2nd ed.), Lexington: D. C. Heath and Company, LCCN 77-171950 PerronGustav Herglotz (1,021 words) [view diff] no match in snippet view article find links to article

students was Emil Artin. Herglotz worked in the fields of seismology, number theory, celestial mechanics, theory of electrons, special relativity, generalDisjunctive sequence (813 words) [view diff] no match in snippet view article find links to article

approximation". In Berthé, Valérie; Rigo, Michael. Combinatorics, automata, and number theory. Encyclopedia of Mathematics and its Applications. 135. Cambridge: CambridgeATS theorem (1,621 words) [view diff] no match in snippet view article find links to article

{\displaystyle i^{2}=-1.} Such sums appear, for example, in number theory in the analysis of the Riemann zeta function, in the solution of problemsHeidelberg University Faculty of Mathematics and Computer Science (351 words) [view diff] no match in snippet view article find links to article

analysis: automorphic functions and modular forms Arithmetic: algebraic number theory, algorithmic algebra, and arithmetical geometry Topology and geometry:Neural cryptography (2,215 words) [view diff] no match in snippet view article find links to article

of these number theory problems are being searched because of this property. Neural key exchange protocol is not based on any number theory. It is basedPoles (10,169 words) [view diff] no match in snippet view article find links to article

theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions, and topology. Stefan Banach, one of the3-manifold (4,830 words) [view diff] no match in snippet view article find links to article

such as knot theory, geometric group theory, hyperbolic geometry, number theory, Teichmüller theory, topological quantum field theory, gauge theoryLeon Ehrenpreis (592 words) [view diff] no match in snippet view article find links to article

Mathematics Genealogy Project Grinberg, Eric L. (2000), Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis, American Mathematical Society,Fuzhou (6,628 words) [view diff] no match in snippet view article find links to article

(陈景润, 1933–1996), mathematician who made significant contributions to number theory Chen Zhangliang (陈章良, 1962–), biologist, elected as vice-governor ofHistory of India (28,910 words) [view diff] no match in snippet view article find links to article

original on 6 December 1998. Retrieved 16 May 2010. Ore, Oystein (1988). Number Theory and Its History. Courier Dover Publications. p. 19. ISBN 978-0-486-65620-5Ricci flow (3,043 words) [view diff] no match in snippet view article find links to article

plane. This topic is closely related to important topics in analysis, number theory, dynamical systems, mathematical physics, and even cosmology. Note thatYoung Scientist and Technology Exhibition (964 words) [view diff] no match in snippet view article find links to article

– A new algorithm versus the RSA Wrote a book on her algorithm and number theory in general, In Code: A Mathematical Journey (ISBN 0-7611-2384-9) FirstAndrew Beal (1,700 words) [view diff] no match in snippet view article find links to article

Independent School District for student use. Beal is self-taught in number theory in mathematics. In 1993, he publicly stated a new mathematical hypothesisDamodar Dharmananda Kosambi (4,422 words) [view diff] no match in snippet view article find links to article

archaeological studies, and contributed in the field of statistics and number theory. His article on numismatics was published in February 1965 in ScientificTimeline of Polish science and technology (4,941 words) [view diff] no match in snippet view article find links to article

theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions and topology; Sierpiński triangle, Sierpiński carpetElementary mathematics (2,486 words) [view diff] no match in snippet view article find links to article

natural numbers such as divisibility and the distribution of prime numbers, are studied in basic number theory, another part of elementary mathematics. Elementary20th century in science (5,663 words) [view diff] no match in snippet view article find links to article

fact incompletable. (Peano arithmetic is adequate for a good deal of number theory, including the notion of prime number.) A consequence of Gödel's twoSobol sequence (1,831 words) [view diff] no match in snippet view article find links to article

(1988). "Low-Discrepancy and Low-Dispersion Sequences", Journal of Number Theory 30: 51–70. Antonov, I.A. and Saleev, V.M. (1979) "An economic methodList of mathematical constants (4,722 words) [view diff] no match in snippet view article find links to article

(2013). The Math Encyclopedia of Smarandache type Notions: Vol. I. Number Theory. David Borwein; Jonathan M. Borwein & Christopher Pinner (1998). ConvergencePisot–Vijayaraghavan number (2,109 words) [view diff] no match in snippet view article find links to article

ISBN 3-7643-2648-4. Peter Borwein (2002). Computational Excursions in Analysis and Number Theory. CMS Books in Mathematics. Springer-Verlag. ISBN 0-387-95444-9. Zbl 1020Lee–Yang theorem (999 words) [view diff] no match in snippet view article find links to article

Press, ISBN 978-0-521-34058-8, MR 1175176 Knauf, Andreas (1999), "Number theory, dynamical systems and statistical mechanics", Reviews in MathematicalIncompressibility method (3,525 words) [view diff] no match in snippet view article find links to article

numbers expressed as binary strings (in the sense of E. Borel) and the distribution of 0s and 1s in binary strings of high Kolmogorov complexity. The basicExplicit formulae (L-function) (2,748 words) [view diff] no match in snippet view article

ISBN 978-0-521-39789-6, MR 1074573, Zbl 0715.11045 Lang, Serge (1994), Algebraic number theory, Graduate Texts in Mathematics, 110 (2nd ed.), New York, NY: Springer-VerlagQuasi-Monte Carlo methods in finance (3,004 words) [view diff] no match in snippet view article find links to article

uniform as possible. It turns out there is a well-developed part of number theory which deals exactly with this desideratum. Discrepancy is a measureAncient Egyptian multiplication (3,180 words) [view diff] no match in snippet view article find links to article

and Wagon, Stan. Old and New Unsolved Problems in Plane Geometry and Number Theory, Mathematical Association of America, 1991. Knorr, Wilbur R. “TechniquesSIC-POVM (3,161 words) [view diff] no match in snippet view article find links to article

Steven; McConnell, Gary; Yard, Jon (2017-04-24). "SICs and Algebraic Number Theory". Foundations of Physics. 47: 1–18. arXiv:1701.05200 . Bibcode:2017FoPhSavilian Professor of Geometry (2,341 words) [view diff] no match in snippet view article find links to article

than 100 joint papers on topics such as distribution of prime numbers, mathematical analysis, analytic number theory, and solving the Waring problem. He alsoCombinatorics on words (2,438 words) [view diff] no match in snippet view article find links to article

Berthé, Valérie; Rigo, Michel, eds. (2010). Combinatorics, automata, and number theory. Encyclopedia of Mathematics and its Applications. 135. Cambridge: CambridgeRomanovski polynomials (1,838 words) [view diff] no match in snippet view article find links to article

(Romanovski in French transcription) within the context of probability distribution functions in statistics. They form an orthogonal subset of a more generalDidier Sornette (9,907 words) [view diff] no match in snippet view article find links to article

real-valued probabilities to probabilities derived from algebraic complex number theory. By its mathematical structure, quantum decision theory aims at encompassingPythagorean astronomical system (1,594 words) [view diff] no match in snippet view article find links to article

that Aristotle was simply having a joke "at the expense of Pythagorean number theory" and that the true function of the Counter-Earth was to balance EarthUniversity of Toronto Department of Mathematics (973 words) [view diff] no match in snippet view article find links to article

“prime spin distribution in number fields, estimates for character sums, applications of sieve methods and quadratic problems in number theory.” Edward BierstoneOhio State University Men's Glee Club (6,627 words) [view diff] no match in snippet view article find links to article

offset the cost of club events. Wardrobe Manager: Responsible for the distribution, collection, and maintenance of uniform components not purchased by groupLee Albert Rubel (3,551 words) [view diff] no match in snippet view article find links to article

difference polynomials and hereditarily irreducible polynomials". Journal of Number Theory. 12 (2): 230–235. doi:10.1016/0022-314X(80)90058-X. Nigel Kalton; LHedonic index (1,405 words) [view diff] no match in snippet view article find links to article

Early History of Price Index Research," Chapter 2 of Essays in Index Number Theory, v. 1, W.E. Diewert and A.O. Nakamura, ed. Elsevier, B.V. Jerry HausmanScale relativity (10,596 words) [view diff] no match in snippet view article find links to article

continuity. El Naschie thus uses a "Cantorian" space-time, and uses mostly number theory (see Nottale 2011, p. 7). This is to be contrasted with scale relativityArthur Engel (mathematician) (1,671 words) [view diff] no match in snippet view article

Engel's 1993 Exploring Mathematics with Your Computer, draws from number theory, probability, statistics, combinatorics, numerical algorithms and manyHerbert Scarf (9,707 words) [view diff] no match in snippet view article find links to article

Mathematics by E.T.Bell. He began reading books on calculus, geometry, number theory, and theoretical mechanics on his own in high school. He was rankedMultiply-with-carry (2,367 words) [view diff] no match in snippet view article find links to article

for a prime p = abr + 1 would reduce considerably the computational number theory required to establish the period of a MWC sequence. Fortunately, a slightList of Italian scientists (3,864 words) [view diff] no match in snippet view article find links to article

mathematician who was awarded the Fields Medal in 1974 for his work in number theory Claudio Bordignon (born 1950), biologist, performed the first procedureZeta function universality (2,416 words) [view diff] no match in snippet view article find links to article

Proceedings of the 7th China–Japan Seminar. The 7th China–Japan Seminar on Number Theory. 11. Fukuoka, Japan: World Scientific. pp. 95–144. arXiv:1407.4216Localization (algebra) (2,699 words) [view diff] no match in snippet view article

Linear Algebraic Groups (2nd ed.). New York: Springer-Verlag. ISBN 0-387-97370-2. Serge Lang, "Algebraic Number Theory," Springer, 2000. pages 3–4.List of Italians (30,716 words) [view diff] no match in snippet view article find links to article

mathematician who was awarded the Fields Medal in 1974 for his work in number theory Claudio Bordignon (born 1950), biologist, performed the first procedureScience and technology in Venezuela (17,336 words) [view diff] no match in snippet view article find links to article

field of Mathematics and two monographs on proofs of primality and number theory. He has been a visiting professor at universities in the United StatesList of atheists in science and technology (24,292 words) [view diff] no match in snippet view article find links to article

Hadamard (1865–1963): French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differentialArtin transfer (group theory) (30,717 words) [view diff] no match in snippet view article

purely group theoretic context, as well as for applications in algebraic number theory concerning Galois groups of higher p-class fields and Hilbert p-classOscillator representation (21,553 words) [view diff] no match in snippet view article find links to article

construction to p-adic Lie groups, showing how the ideas could be applied in number theory, in particular to give a group theoretic explanation of theta functionsMathematical Grammar School (6,943 words) [view diff] no match in snippet view article find links to article

statistics, mathematical analysis, numerical analysis, combinatorics, number theory, geometry, linear algebra, analytical geometry, algebra, various advanced