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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 (5,734 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 (9,885 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 can be expressed as a product of primesSmooth number (1,177 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 (3,776 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 DiophantusRiemann zeta function (7,054 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 LogarithmicNatural number (3,803 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 matrix (3,325 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 overList of complex analysis topics (367 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 (2,301 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) (4,555 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 positiveHermann Weyl (3,879 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 zetaCarmichael number (2,519 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 modularAbstract analytic number theory (1,209 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 toRiemann hypothesis (14,041 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 GourdonGreek letters used in mathematics, science, and engineering (3,676 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 microlitreList of mathematical functions (947 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; importantUnusual 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' number (1,561 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 forRiemann–von Mangoldt formula (277 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 theCramér's conjecture (1,235 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 consecutiveHilbert's eighth problem (184 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 concernedDigit 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 ofPrime 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 overlapElliott–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 applicationsGaussian integer (1,407 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 additionBombieri–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, averagedTotative (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) countsList of inequalities (670 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–TISPi (16,015 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. It is also found in cosmology, thermodynamics, mechanicsP-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 numbersBrun–Titchmarsh theorem (381 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 primeVojta'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 diophantineErdős 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 arcsineL-function (918 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-seriesPál Turán (1,173 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 inList of things named after Carl Friedrich Gauss (730 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 connectionElliptic 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 numbersMultiplicative 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 usuallySageMath (1,884 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 FebruaryPrime-counting function (3,066 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 conjecturedWolfgang 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 subspaceCyclotomic unit (357 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)−1Wolfgang 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 subspaceBinomial number (443 words) [view diff] no match in snippet view article find links to article

Not to be confused with Binomial distribution. In mathematics, specifically in number theory, a binomial number is an integer which can be obtained byHarmonic number (4,939 words) [view diff] no match in snippet view article find links to article

were studied in antiquity and are important in various branches of number theory. They are sometimes loosely termed harmonic series, are closely relatedBateman–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, namedQuadratic 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 {\displaystyleGeorge Pólya (1,549 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 hisSchwartz–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–BruhatBernhard Riemann (2,467 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 mostlyDirichlet's theorem on arithmetic progressions (2,770 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, thereSerge Lang (1,915 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 AlgebraNumber (6,336 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 usesMikio Sato (272 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 beenLeonhard Euler (7,056 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 andE (mathematical constant) (4,866 words) [view diff] no match in snippet view article

article: Standard normal distribution The simplest case of a normal distribution is known as the standard normal distribution, described by this probabilityList 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 (probabilityChebotarev's density theorem (2,020 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 fieldIllegal 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 primesEquidistributed sequence (2,089 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 sequencePrimecoin (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 portalGamma function (9,439 words) [view diff] no match in snippet view article find links to article

function of ordinals, see Veblen function. For the gamma distribution in statistics, see Gamma distribution. In mathematics, the gamma function (representedGillies' conjecture (422 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 inHarold 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 AccringtonAkshay Venkatesh (819 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 ergodicLists of mathematics topics (2,224 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 andDiscrete mathematics (3,121 words) [view diff] no match in snippet view article find links to article

is basically enumerative combinatorics. Main article: Number theory Number theory is concerned with the properties of numbers in general, particularlyBarban–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 (845 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 toQuadratic residue (5,537 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 integerMellin transform (2,490 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 (661 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 theHeath-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=X1X2X3Logarithm (10,727 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 theoryDirichlet density (611 words) [view diff] no match in snippet view article find links to article

This article is not about the Dirichlet distribution of probability theory. In mathematics, the Dirichlet density (or analytic density) of a set of primesStoneham number (187 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 MathematicsNormal number (4,000 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 1-56881-162-4Maier'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 hypothesisHans 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-UniversitätManin 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 numberWilliam 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 textbooksKohji 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 forConjecture (2,564 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 theoristsChampernowne constant (989 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.; NicolasEdmund 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 BerlinHecke character (1,717 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 largerList 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'sEuclidean algorithm (14,023 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 factorizationsEuler's totient function (6,198 words) [view diff] no match in snippet view article find links to article

"Φ(n)" redirects here. For other uses, see phi. In number theory, Euler's totient function counts the positive integers up to a given integer n thatSolomon W. Golomb (827 words) [view diff] no match in snippet view article find links to article

in 1953. He has specialized in problems of combinatorial analysis, number theory, coding theory, and communications. His game of pentomino inspired TetrisMertens conjecture (1,197 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 MSinkov 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 combinatoricsNormal distribution (18,437 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, whichPerfect 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 toMontgomery'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 MathematicalHelmut Maier (609 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"Exponential 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 startedMatsumoto 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,Cubic 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 extensionP-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 pDivisor 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 asymptoticYuri Linnik (456 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 inRobert 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 laterPartition function (mathematics) (3,335 words) [view diff] no match in snippet view article

For the partition function in number theory, see Partition (number theory). The partition function or configuration integral, as used in probability theoryGumbel distribution (1,417 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 partition of an integerPeter Gustav Lejeune Dirichlet (3,242 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 andKarl 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, PrimzahlverteilungList of mathematical theories (171 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 PerturbationBasel problem (2,744 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 EulerHaar measure (3,500 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, and ergodic 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 (613 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:Augustin-Louis Cauchy (5,366 words) [view diff] no match in snippet view article find links to article

lunar crater, see Cauchy (crater). For the statistical distribution, see Cauchy distribution. For the condition on sequences, see Cauchy sequence. BaronAbc conjecture (3,984 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). ItElectrical network (909 words) [view diff] no match in snippet view article find links to article

For electrical power transmission grids and distribution networks, see Electrical grid. An electrical network is an interconnection of electricalRoth's theorem (1,053 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 (3,449 words) [view diff] no match in snippet view article find links to article

Not to be confused with regular number. In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to proveCarl Friedrich Gauss (7,156 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, geophysicsTimeline 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 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 primesGraham Everest (275 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 MathematicalFlorian Luca (329 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 functionsFerdinand Georg Frobenius (1,095 words) [view diff] no match in snippet view article find links to article

Frobenius class in the Galois group is p mod m. From this point of view, the distribution of Frobenius conjugacy classes in Galois groups over Q (or, more generallyRational point (817 words) [view diff] no match in snippet view article find links to article

In number theory, a rational point is a point in space each of whose coordinates are rational; that is, the coordinates of the point are elements of theVon Mangoldt function (1,357 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, physicsPierre 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 theHua Luogeng (1,684 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 educationTimothy 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 toElementary proof (617 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 timePractical 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 (163 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 reviewsElliptic 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 (1,186 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 functionsComplex number (10,510 words) [view diff] no match in snippet view article find links to article

used to classify sums of squares. Main article: Analytic number theory Analytic number theory studies numbers, often integers or rationals, by taking advantageTibor 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 undergraduateAdrien-Marie Legendre (1,639 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 numberPan Chengdong (271 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 ShandongPéter 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 achievementsRodion 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 1928Change-making problem (1,302 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 (7,059 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 betweenNick 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 PrincetonHarald Cramér (1,086 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. HisTranscendental number (4,608 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 theoryLegendre's constant (559 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 (Vera T. Sós (824 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 bothRegular (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 theHilbert–Pólya conjecture (1,189 words) [view diff] no match in snippet view article find links to article

statements. He gives a geometric interpretation of the explicit formula of number theory as a trace formula on noncommutative geometry of Adele classes. A possibleUlam spiral (2,150 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 hasKlaus Roth (382 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 birthdayRamin 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 TheoryMark 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 NottinghamPoisson summation formula (2,851 words) [view diff] no match in snippet view article find links to article

{\displaystyle f=0\,} (Pinsky 2002). In number theory, Poisson summation can also be used to derive a variety of functionalList of important publications in mathematics (9,484 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 DirichletPrime gap (2,908 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 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 formulatingEuler–Mascheroni constant (4,257 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 definedIlya 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 contributionList of mathematical symbols (991 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. (ThisGlossary of areas of mathematics (5,653 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 variousKolakoski sequence (887 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: AmericanStatistics (7,395 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 toolsJonas Kubilius (1,091 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 termHee 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 extensivelyProbabilistic method (1,652 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 (eProblems involving arithmetic progressions (565 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 (12,256 words) [view diff] no match in snippet view article find links to article

numbers Bn are a sequence of rational numbers with deep connections to number theory. The values of the first few Bernoulli numbers are B0 = 1, B± 1 = ±1/2Unit fraction (1,070 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 conjectureFermat pseudoprime (1,885 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 (227 words) [view diff] no match in snippet view article find links to article

Permutations Proportion Rounding Scientific notation Main article: Outline of number theory Riemann zeta function L-functions Multiplicative functions Modular formsRefactorable number (413 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 computerLaplace–Stieltjes transform (1,338 words) [view diff] no match in snippet view article find links to article

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 . GrimmettJacques Hadamard (1,830 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 (2,061 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, whichVinogradov's theorem (988 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 SeriesBeurling zeta function (223 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 primeZeta function regularization (2,135 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 functionFields Medal (2,444 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, USContributions of Leonhard Euler to mathematics (2,115 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. InAlexandru 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 knownRSA (cryptosystem) (7,334 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 exponentiationSylvester Medal (491 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 generalPaul T. Bateman (592 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 translationHarald 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 (838 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 (16,868 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 (540 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.Outline of science (8,841 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 usesTheorem (3,602 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 proofNevanlinna theory (2,579 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 toolHistory of mathematics (12,491 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 orderRichard Garfield (1,280 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)90078-4Khinchin'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 UniversityGérald 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 andGiuseppe Melfi (469 words) [view diff] no match in snippet view article find links to article

sequences having polynomial growth. Among other problems in elementary number theory, he is the author of a theorem that allowed him getting a 5328-digitClosed-form expression (1,380 words) [view diff] no match in snippet view article find links to article

mathematical modelling and computer simulation. See also: Transcendental number theory Three subfields of the complex numbers C have been suggested as encodingBell number (3,919 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. Main article: PartitionErgodic theory (3,499 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). Main article:Rule 90 (3,240 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 (1,310 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 AmericanHenri Poincaré (8,660 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 (1,441 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 ) =Public-key cryptography (7,165 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. RetrievedHurwitz zeta function (3,058 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 alsoLiouville number (3,142 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 withKummer sum (731 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, againWallenius' 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 (4,667 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) (1,943 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 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 andMichał Kalecki (6,283 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 (2,480 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, 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 biquadraticSigma (1,020 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 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 ofNoncentral 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 inFrench 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; CharlesPythagorean triple (9,675 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 . ForD. R. Kaprekar (987 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 theFeedback 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 integerPartition problem (2,307 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 integersList of victims of Nazism (203 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 1868–1942Golden ratio (10,457 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 978-0-521-85014-8Ideal lattice cryptography (5,742 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 placeMillennium Prize Problems (1,137 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 problemErdős–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 MathematicalBc (programming language) (1,666 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 particlePolylogarithm (9,103 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 ColloquiumThe Art of Computer Programming (2,706 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 1.2Number sign (3,512 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 fileHà 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. EsseenExplicit formulae (L-function) (2,735 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-VerlagExplicit formulae (L-function) (2,735 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-VerlagMathematics Subject Classification (1,335 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 algebrasHardy–Littlewood tauberian theorem (1,202 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, MichielFreeman Dyson (7,975 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. In 1947, Dyson moved to the United States as a Commonwealth FellowGeneralized function (2,181 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 onNeural 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 basedLambda (2,130 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. Lambda is a symbol associated with the Identitarian movement, intendedLatin letters used in mathematics (2,345 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 timeComplexity function (1,302 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: CambridgeNaor–Reingold pseudorandom function (1,936 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–ReingoldAlexander Grothendieck (6,384 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)List of algorithms (7,526 words) [view diff] no match in snippet view article find links to article

Algorithm: create voronoi diagram Quasitriangulation Further information: Number theory Binary GCD algorithm: Efficient way of calculating GCD. Booth's multiplicationDiffie–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 2005-11-23Almost surely (1,622 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"Generalized Riemann hypothesis (1,300 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. GraduateDifferential equation (3,881 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 Computation ControlMiller–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 (AugustThue–Morse sequence (2,985 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 wasGustav Herglotz (520 words) [view diff] no match in snippet view article find links to article

Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electronsVector space (11,644 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 theJohn von Neumann (14,789 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 askedEdgar Gilbert (1,513 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, andErdős–Bacon number (3,529 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)80027-5Mathematical 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 organizationsGovernment Communications Headquarters (6,129 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 feasibleIreland (18,073 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 compositeHistory of cryptography (5,846 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:John McKay (mathematician) (2,206 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 (10,198 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 1989Leon 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,Automatic sequence (1,667 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 theoryRiesz mean (727 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 aRoyal Medal (340 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 celebratedTimeline of mathematics (6,845 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 introducesTaylor's law (13,596 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 MertensJean-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 nombresList 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. pFuzhou (5,931 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 ofSPECfp (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 primalityArithmetic Fuchsian group (3,796 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. Katz, M.; Schaps, M.; Vishne, U. (2007). "LogarithmicFourier analysis (4,079 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, imaging, probability theory, statisticsFeynman–Kac formula (1,869 words) [view diff] no match in snippet view article find links to article

2307/1990512. JSTOR 1990512. This paper is reprinted in Mark Kac: Probability, Number Theory, and Statistical Physics, Selected Papers, edited by K. Baclawski andExpander graph (2,582 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, CambridgeBuckeye 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 receivedCounter-Earth (2,926 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 (901 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) Lessons on the theory of functions (1898)Matrix (mathematics) (12,105 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 physicsDisjunctive sequence (811 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: CambridgeFibonacci word (1,629 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: CambridgeBinary logarithm (4,721 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 applicationsContinued fraction (7,616 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 PerronHeidelberg University Faculty of Mathematics and Computer Science (361 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:ATS 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 problemsIncompressibility 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 basic3-manifold (4,966 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 theoryDamodar Dharmananda Kosambi (4,172 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 ScientificHistory of India (26,819 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 (3,057 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 thatUniversity 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 BierstoneYoung Scientist and Technology Exhibition (953 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) FirstSobol sequence (1,810 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 (2,112 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 1020Mathematical constants and functions (4,663 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 MathematicalVolkenborn 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 276Andrew Beal (1,695 words) [view diff] no match in snippet view article find links to article

student use. Main article: Beal conjecture Beal is self-taught in number theory in mathematics. In 1993, he publicly stated a new mathematical hypothesisRomanovski polynomials (1,893 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 generalAncient 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. “TechniquesSavilian Professor of Geometry (2,377 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 alsoElementary mathematics (3,606 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. ElementaryQuasi-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 (1,587 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 EarthCombinatorics on words (2,462 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: CambridgeList of Italian scientists (3,786 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 procedureLee 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 (6,384 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 (10,600 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 relativityMultiply-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 slightHerbert 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 rankedArthur Engel (mathematician) (1,672 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 manyLocalization (algebra) (2,686 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 (30,579 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 procedureList of atheists in science and technology (24,547 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 (21,549 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 functionsMatematička gimnazija (6,963 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