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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 ofPrime number theorem (5,743 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 formalizesPrime number (9,938 words) [view diff] no match in snippet view article find links to article

fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 is either a prime itself or can be expressedSmooth number (1,193 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. The term seems to have been coined byDiophantine 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 DiophantusNatural number (3,913 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, suchRandom number generation (3,799 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 transformRandom matrix (3,345 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 eigenvaluesSupersingular 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 overHarmonic analysis (1,053 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, tidalList 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. ISBN 978-1-4757-5194-9. doi:10.1007/978-1-4757-5194-9Erdős–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,Hermann Weyl (3,848 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 zetaPartition (number theory) (4,649 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 positiveAbstract 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 toGreek letters used in mathematics, science, and engineering (3,559 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 microlitreCharacter sum (690 words) [view diff] no match in snippet view article find links to article

1007/BF01390204. Hugh L. Montgomery; Robert C. Vaughan (2007). Multiplicative number theory I. Classical theory. Cambridge tracts in advanced mathematics. 97. CambridgeSkewes' number (1,576 words) [view diff] no match in snippet view article find links to article

In number theory, Skewes' number is any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds forUnusual 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 thanRiemann–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 theHilbert'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 concernedPrime 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 overlapTotative (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) countsCramér's conjecture (1,200 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 consecutiveElliott–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 applicationsDigit 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 ofRiemann hypothesis (14,038 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 GourdonCarmichael number (2,713 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 modularVojta'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 numbersBombieri–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, averagedErdős 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 (1,158 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 inBrun–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 primeRiemann zeta function (8,222 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 LogarithmicL-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-seriesElliptic 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 numbersList of things named after Carl Friedrich Gauss (744 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 connectionMultiplicative 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 usuallyCyclotomic 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)−1Discrete mathematics (3,057 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 areSageMath (1,906 words) [view diff] no match in snippet view article find links to article

mathematics, including algebra, combinatorics, numerical mathematics, number theory, and calculus. The first version of SageMath was released on 24 FebruaryGoldbach's conjecture (2,765 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 2List 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–TISPrime-counting function (3,063 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 conjecturedBateman–Horn conjecture (998 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, namedWolfgang M. Schmidt (311 words) [view diff] no match in snippet view article find links to article

Academy of Sciences. He was awarded the eighth Frank Nelson Cole Prize in Number Theory for work on Diophantine approximation. He is known for his subspacePrimecoin (792 words) [view diff] no match in snippet view article find links to article

Official website Anarchism portal Cryptography portal Economics portal Free software portal Internet portal Number theory portal Numismatics portalQuadratic residuosity problem (1,144 words) [view diff] no match in snippet view article find links to article

The quadratic residuacity problem in computational number theory is to decide, given integers a {\displaystyleHarmonic number (4,792 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 relatedSchwartz–Bruhat function (372 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–BruhatPi (17,352 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 ubiquityBernhard Riemann (2,432 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 mostlyNumber (6,653 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 usesDirichlet'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, thereGeorge Pólya (1,554 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 hisList of things named after Peter Gustav Lejeune Dirichlet (192 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 (1,900 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 AlgebraChebotarev's density theorem (2,021 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 fieldConjecture (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 (2,098 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 sequenceEffective 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 toMikio Sato (349 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 beenIllegal 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 jurisdiction. One of the first illegal primesHarold Davenport (811 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 1-56881-162-4Lists of mathematics topics (2,197 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 andGillies' 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 inMaier'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 numbersHelge von Koch (402 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 hypothesisStoneham 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 MathematicsE (mathematical constant) (4,809 words) [view diff] no match in snippet view article

chance of winning. Playing one million times is modelled by the binomial distribution, which is closely related to the binomial theorem. The probability ofHeath-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=X1X2X3Mellin 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; itFiroozbakht's conjecture (660 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 theQuadratic 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 integerManin 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 numberHans Rademacher (534 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-UniversitätHee 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 extensivelyKohji 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 forEdmund Landau (576 words) [view diff] no match in snippet view article find links to article

February 1938) was a German born mathematician who worked in the fields of number theory and complex analysis. Edmund Landau was born to Jewish family in BerlinChampernowne constant (1,096 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.; NicolasHecke character (1,718 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 largerEuler's totient function (6,133 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 theEuclidean algorithm (13,975 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 factorizationsMertens conjecture (1,194 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 MExponential 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 startedAkshay Venkatesh (894 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 ergodicNormal number (3,992 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 1-56881-162-4List 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'sList 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 PerturbationLogarithm (10,833 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 theoryNick Katz (621 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 PrincetonSinkov 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 combinatoricsPerfect 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 toNormal distribution (19,601 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, whichP-adic order (761 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 pMatsumoto 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,Solomon W. Golomb (839 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 TetrisPeter Gustav Lejeune Dirichlet (3,220 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 andHelmut Maier (620 words) [view diff] no match in snippet view article find links to article

(2015). Analytic Number Theory. Springer, New York. pp. v–vi. Granville, Andrew (1994). "Unexpected irregularities in the distribution of prime numbers"William 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 textbooksCubic 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 extensionMontgomery's pair correlation conjecture (818 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 MathematicalYuri 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 inGumbel distribution (1,409 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 ofRobert Alexander Rankin (388 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's father, the Revd Oliver Shaw Rankin, was a minister who laterKaisa 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 ResearchKarl 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, PrimzahlverteilungDivisor summatory function (1,780 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 asymptoticHaar measure (4,072 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 theoryOn 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 duringLiouville 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:Elliptic unit (354 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: Modular unit Coates, J.H.; GreenbergLeonhard Euler (7,091 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 andAbc conjecture (4,089 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). ItRoth'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 typeRegular prime (3,226 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.Basel problem (2,729 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 EulerTimeline of number theory (716 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 multiplicationRamin 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 TheoryMaier'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 primesGraham 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 MathematicalChebyshev'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 theFlorian Luca (324 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 functionsCarl Friedrich Gauss (7,145 words) [view diff] no match in snippet view article find links to article

mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysicsElementary 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 timeTimothy Browning (214 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 toPierre 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 theVon 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, physicsGamma function (9,611 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 identitiesPractical number (2,743 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 sumsNumber Theory: An Approach through History from Hammurapi to Legendre (187 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 reviewsHua 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 educationAdrien-Marie Legendre (1,673 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 undergraduateChange-making problem (1,293 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 likewiseBig O notation (6,953 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 betweenComplex number (10,570 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 forPhi (1,165 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 functionsUlam spiral (2,175 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 hasPan 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 ShandongRodion Kuzmin (406 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. In 1928Regular (957 words) [view diff] no match in snippet view article find links to article

matrix (disambiguation) Regular code, an algebraic code with a uniform distribution of distances between codewords Regular graph, a graph such that all theHarald 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. HisLegendre's constant (554 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 (Poisson summation formula (2,851 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 functionalVera 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 bothKlaus Roth (375 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 birthdayMark 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 NottinghamHilbert–Pólya conjecture (1,332 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 directorGaussian integer (5,258 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 formulatingList of important publications in mathematics (9,467 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 DirichletEuler–Mascheroni constant (4,266 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 definedPrime gap (2,839 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 favouritePaul T. Bateman (590 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 translationTranscendental number (4,676 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 number theoryPéter Kiss (mathematician) (594 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 achievementsIlya Piatetski-Shapiro (2,118 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 contributionGlossary of areas of mathematics (5,857 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 variousList of mathematical symbols (999 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. (ThisJonas Kubilius (1,098 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 termStatistics (7,302 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 toolsProblems involving arithmetic progressions (559 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 pointsProbabilistic 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 (eBernoulli number (11,714 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 tableFermat pseudoprime (1,881 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 theoremOutline of arithmetic (220 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 formsLaplace–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 . GrimmettUnit 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 conjectureRefactorable number (420 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 computerJacques Hadamard (1,821 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 differentialTwin prime (2,093 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, whichFields Medal (2,754 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 University, USVinogradov'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 numbersRamanujan'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 SeriesGérald Tenenbaum (408 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 andBeurling 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 primeSylvester 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 generalContributions 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. InZeta 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 functionRSA (cryptosystem) (7,500 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 exponentiationLatin letters used in mathematics (2,381 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 timeHarald 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:Glossary of arithmetic and diophantine geometry (4,887 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 proposedS.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 anFourier transform (16,775 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 formulaCousin 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.Theorem (3,573 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 proofOutline of science (8,767 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 usesHistory of mathematics (12,818 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 orderKhinchin'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 haveWilliam 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 UniversityNevanlinna 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 toolRichard Garfield (1,271 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 (431 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-digitErgodic 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). ErgodicBell number (3,913 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 generalRule 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 different1935 in science (1,319 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 AmericanPublic-key cryptography (7,183 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. RetrievedHenri Poincaré (8,709 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 theoryMertens function (1,440 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 ) =Augustin-Louis Cauchy (5,502 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 CauchyAlmost surely (1,246 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"Hurwitz 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 alsoKummer 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, againLiouville number (3,144 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 withErdős–Bacon number (3,798 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)80027-5Wallenius' 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 staticticsElliptic 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 EdMaple (software) (2,231 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 GroupArs Conjectandi (3,933 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 areLambda (1,875 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 variance1837 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 andMichał Kalecki (6,731 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 relieveNoncentral hypergeometric distributions (2,353 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 inFisher's noncentral hypergeometric distribution (2,480 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, AList of mathematical proofs (605 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 ofSigma (1,023 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 aD. R. Kaprekar (971 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 theFelix 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 biquadraticPythagorean triple (9,719 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 . ForFrench mathematical seminars (313 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; CharlesIdeal lattice cryptography (5,741 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 placeThe Art of Computer Programming (2,865 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 1.2Partition problem (2,316 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 MathematicalGolden ratio (10,101 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 978-0-521-85014-8Feedback with Carry Shift Registers (994 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 integerPolylogarithm (9,128 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 ColloquiumBc (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 particleMillennium Prize Problems (1,305 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 problemHà Huy Khoái (803 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 JCarl-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. EsseenNumber sign (3,541 words) [view diff] no match in snippet view article find links to article

topology), where A and B are knots, A#B is the knots' knot sum. In number theory, n# is the primorial of n. In many scripting languages and data fileCryptography (8,602 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 ofMathematics Subject Classification (1,339 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 algebrasExplicit formulae (L-function) (2,809 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-VerlagHardy–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, MichielGeneralized 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 onFreeman Dyson (7,945 words) [view diff] no match in snippet view article find links to article

resigned his professorship in 1947. In 1947, he published two papers in number theory. Friends and colleagues describe Dyson as shy and self-effacing, withQuantum Bayesianism (7,509 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. Bibcode:2017FoPh..tmp...34A. ISSN 0015-9018Neural cryptography (2,033 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 basedClosed-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 majorComplexity 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: CambridgeMiller–Rabin primality test (3,176 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 (AugustNaor–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–ReingoldGeneralized Riemann hypothesis (1,311 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. GraduateAlexander Grothendieck (6,629 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)Differential equation (3,875 words) [view diff] no match in snippet view article find links to article

Areas Algebra elementary linear multilinear abstract Arithmetic / Number theory Calculus / Analysis Category theory Combinatorics Group theory ComputationThue–Morse sequence (3,070 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 wasJohn von Neumann (14,949 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 askedKolakoski sequence (3,064 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: AmericanIreland (18,432 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 organizationsEdgar Gilbert (1,358 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, andQuaternion (10,273 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 1989John McKay (mathematician) (2,207 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. MR 0527761. doi:10.1016/0022-314X(79)90020-9. McKayLeon 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,Riesz mean (736 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 aVector space (11,549 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 theList 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 1868–1942Royal 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 celebratedJean-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 nombresTaylor's law (12,423 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 MertensTed Kaczynski (10,830 words) [view diff] no match in snippet view article find links to article

Sutcliffe" (PDF). Mathematics Magazine, 41(2), 84-86. A brief paper in number theory concerning the digits of numbers. —— (March 1969). "Boundary FunctionsWu Chinese-speaking people (2,672 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 educationArithmetic Fuchsian group (3,788 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,Chebyshev 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. pList 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 JuliusPoles (7,464 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 Hilary Koprowski, virologistTimeline of mathematics (7,035 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 introducesFeynman–Kac formula (1,956 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:Glossary of artificial intelligence (1,146 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 numberSPECfp (711 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 primalityFourier analysis (4,049 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, probabilityExpander graph (2,681 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, CambridgeCounter-Earth (2,335 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'Émile Borel (912 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)Buckeye TV (2,147 words) [view diff] no match in snippet view article find links to article

special videos at the request of Ohio State President Gordon Gee for distribution among the student body. One such video, "Study Team Delta", has receivedMatrix (mathematics) (12,048 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 (7,985 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 afterBinary 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 (1,630 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 (843 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 (7,555 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 PerronHistory of cryptography (6,006 words) [view diff] no match in snippet view article find links to article

"Combinational analysis, numerical analysis, Diophantine analysis and number theory." Taken from Encyclopedia of the History of Arabic Science, Volume 2:Government Communications Headquarters (6,286 words) [view diff] no match in snippet view article find links to article

H. Ellis, a GCHQ staff member since 1952, who lacked the necessary number theory expertise necessary to build a workable system. Subsequently, a feasibleDisjunctive 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: CambridgeHeidelberg 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:Gustav Herglotz (1,020 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, generalATS 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 problems3-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 theoryHistory of India (27,533 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 978-0-486-65620-5Incompressibility method (3,385 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 basicFuzhou (6,543 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 ofRicci flow (3,039 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 thatDamodar Dharmananda Kosambi (4,156 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 ScientificYoung Scientist and Technology Exhibition (949 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) FirstTimeline of Polish science and technology (4,865 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. ElementarySobol sequence (1,830 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 methodPisot–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 1020Romanovski polynomials (1,784 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 generalVolkenborn 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 276Mathematical constants and functions (4,695 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). ConvergenceLee–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 MathematicalAndrew Beal (1,702 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 hypothesisAncient Egyptian multiplication (3,166 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 (2,990 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. Bibcode:2017FoPh..tmp...34A. ISSN 0015-9018Savilian 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 alsoQuasi-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 measurePythagorean astronomical system (1,581 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 BierstoneCombinatorics on words (2,450 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: CambridgeDidier Sornette (9,622 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 encompassingLee Albert Rubel (3,546 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; LOhio 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 groupHedonic index (1,394 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 (10,612 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 relativityHerbert Scarf (9,702 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 (2,386 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 slightArthur Engel (mathematician) (1,680 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 manyList of Italian scientists (3,858 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. ISBN 978-981-4644-92-1Localization (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 (30,544 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 (15,847 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 (24,352 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-classMathematical Grammar School (6,895 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