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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 (5,711 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 formalizesSmooth 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 DiophantusPrime number (9,853 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 primesList 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 hydrodynamicsSupersingular 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 overAbstract 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 toSkewes' number (1,551 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 forErdős–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,Random matrix (3,319 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 eigenvaluesList 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–TISErdős 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 arcsineP-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 numbersTotative (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) countsRiemann–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 theNatural number (3,764 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, suchCharacter 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. CambridgePrime geodesic (695 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 overlapUnusual 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 thanBrun–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 primeSquare-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 978-1-4757-5194-9Hilbert'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 concernedVojta'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 diophantineBombieri–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, averagedPartition (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 positiveList of mathematical functions (963 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; importantMultiplicative 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 (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)−1Cramér's conjecture (1,230 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 (652 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 applicationsBinomial 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 byDigit 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 zeta function (7,058 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 LogarithmicGreek 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 microlitreCarmichael number (2,485 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 modularGillies' 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 inList 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 (probabilitySchwartz–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–BruhatHermann Weyl (3,878 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 zetaPál 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 inElliptic 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 numbersGaussian 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 additionWolfgang 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 subspaceBateman–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 {\displaystyleQuadratic 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 {\displaystyleRiemann hypothesis (13,960 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 GourdonBarban–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 1-56881-162-4L-function (911 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-seriesEffective 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 toSageMath (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 FebruaryDirichlet 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 primesGoldbach's conjecture (2,754 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 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 connectionStoneham 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 MathematicsChampernowne constant (795 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.; NicolasManin 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 numberHeath-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=X1X2X3Prime-counting function (3,060 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 conjecturedChebotarev's density theorem (2,018 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 field Q ofPartition 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 theoryPrimecoin (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 portalAkshay 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 ergodicBernhard Riemann (2,471 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, thereMikio 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 beenElliptic 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.; GreenbergWilliam 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 textbooksGeorge 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 hisHarold 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 AccringtonKohji 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 forEquidistributed 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 sequenceSerge 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 AlgebraIllegal 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 primesMatsumoto 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,Hans 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-UniversitätSinkov 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 combinatoricsFiroozbakht'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 theHarmonic number (4,835 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 relatedPeter Gustav Lejeune Dirichlet (3,192 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 andHecke 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 largerLists 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 andMellin 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; itKarl 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, PrimzahlverteilungMertens 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 MHelge 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 hypothesisExponential 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 startedList 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 PerturbationNumber Theory: An Approach through History from Hammurapi to Legendre (136 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 reviewsQuadratic residue (5,532 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 integerHelmut 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"P-adic order (680 words) [view diff] no match in snippet view article find links to article

In number theory, for a given prime number p, the p-adic order or p-adic additive valuation of a non-zero integer n is the highest exponent ν such thatDiscrete 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, particularlyCubic 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 extensionEdmund Landau (572 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 BerlinMontgomery'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 MathematicalP-adic order (680 words) [view diff] no match in snippet view article find links to article

In number theory, for a given prime number p, the p-adic order or p-adic additive valuation of a non-zero integer n is the highest exponent ν such thatCubic 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 extensionFlorian 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 functionsList 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'sTimeline 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 multiplicationYuri 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 inOn 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 duringGraham 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 MathematicalDivisor 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 asymptoticEuler'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 thatChebyshev'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 theTimothy 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 toNormal number (3,990 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 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 primesPerfect 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 toConjecture (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 theoristsRobert 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 laterGumbel 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 integerRamin 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 TheoryLiouville 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:Paul 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 translationLogarithm (10,698 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 theoryEuclidean algorithm (13,989 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 factorizationsRoth'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 typeSolomon 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 TetrisRegular 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 proveElementary 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 timeBasel problem (2,748 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 EulerPéter 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 achievementsNumber (6,339 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 usesRodion 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 1928Leonhard Euler (7,048 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 andTibor Šalát (396 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 undergraduateAbc conjecture (3,988 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). ItJonas 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 termPierre François Verhulst (422 words) [view diff] no match in snippet view article find links to article

Brussels – 15 February 1849, Brussels) was a mathematician and a doctor in number theory from the University of Ghent in 1825. Verhulst published in 1838 theGamma function (9,115 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 (representedPan 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 ShandongRational 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 theHaar 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 theoryChange-making problem (1,332 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 likewiseFerdinand 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 generallyVon 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, physicsElectrical 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 electricalPractical number (2,742 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 sumsPi (15,932 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, mechanicsMark Pollicott (214 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 NottinghamMark Pollicott (214 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 NottinghamLegendre'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 (Hua 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 educationAugustin-Louis Cauchy (5,363 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. BaronCarl Friedrich Gauss (7,157 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, geophysicsVera 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 bothAdrien-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 numberFermat pseudoprime (1,691 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 theoremPaul 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 formulatingPoisson summation formula (2,849 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 functionalHilbert–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 possibleNick Katz (620 words) [view diff] no match in snippet view article find links to article

particularly on p-adic methods, monodromy and moduli problems, and number theory. He is currently a professor in the Mathematics Department at PrincetonBig O notation (6,948 words) [view diff] no match in snippet view article find links to article

algorithm changes as the problem size becomes extremely large. In analytic number theory it is used to estimate the "error committed" while replacing the asymptoticComplex number (10,544 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 advantageHarald 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. HisGlossary of areas of mathematics (5,620 words) [view diff] no match in snippet view article find links to article

modern algebra. Abstract analytic number theory: a branch mathematics that take ideas from classical analytic number theory and applies them to various otherProblems 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 pointsKolakoski 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: AmericanRefactorable 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 computerList of important publications in mathematics (9,483 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 DirichletPhi (1,121 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 functionsKlaus 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 birthdayIlya 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 contributionHarald 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:Laplace–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 . GrimmettTranscendental number (4,595 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 theoryAlexandru 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 knownOutline 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 formsRamanujan'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 SeriesVinogradov'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 numbersBeurling 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 primeWilliam 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 UniversityUnit 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 conjecturePrime gap (2,832 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 favouriteS.I.N. Theory (836 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 anBernoulli 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 = ±1/2List of mathematical symbols (989 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. (ThisContributions 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. InEuler–Mascheroni constant (4,279 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 definedSylvester 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 generalJacques 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 differentialHee Oh (465 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 extensivelyZeta 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 functionGlossary 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 proposedKhinchin's constant (1,334 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 haveTwin prime (2,167 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, whichGérald 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 andStatistics (7,389 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 toolsGiuseppe 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-digitCousin 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.RSA (cryptosystem) (7,250 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 exponentiationRule 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 differentFourier transform (16,856 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 formulaNevanlinna 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 toolTheorem (3,603 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 (8,845 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 usesWallenius' 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 staticticsThue–Morse sequence (2,956 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 wasHistory of mathematics (12,510 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 orderBell number (3,912 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: PartitionKummer 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, againClosed-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 encoding1935 in science (1,306 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 AmericanNoncentral 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 inErgodic theory (3,433 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:Fisher'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, AFields Medal (2,481 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, USMertens 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 (7,202 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 withMichał 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 relieveFelix 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 biquadraticFrench 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; Charles1837 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 andElliptic curve primality (4,666 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 EdIdeal 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 placeArs 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 areList 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 ofCarl-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. EsseenD. R. Kaprekar (976 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 theErdős–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 MathematicalHà 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 JLambda (2,101 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, intendedFeedback 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 integerHenri Poincaré (8,644 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 theoryChebyshev 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. pPartition 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 integersPythagorean triple (9,597 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 . ForMillennium Prize Problems (1,100 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 problemComplexity 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: CambridgeUlam spiral (1,857 words) [view diff] no match in snippet view article find links to article

1090/S0025-5718-02-01418-7 Guy, Richard K. (2004), Unsolved problems in number theory (3rd ed.), Springer, p. 8, ISBN 978-0-387-20860-2 Gardner, M. (MarchHardy–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, MichielList 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 1868–1942The Art of Computer Programming (2,645 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 1.2Richard Garfield (1,276 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)90078-4Bc (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 particleNaor–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–ReingoldNumber sign (3,555 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 fileMathematics 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 algebrasPolylogarithm (9,102 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 ColloquiumGeneralized 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 basedFreeman Dyson (7,854 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 FellowMathematical 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 organizationsTaylor's law (13,580 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 MertensDiffie–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 2005-11-23Generalized 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. GraduateAlmost 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"Differential equation (3,847 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 ControlAlexander Grothendieck (6,374 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)Erdős–Bacon number (3,523 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)80027-5List of algorithms (7,525 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 multiplicationVector space (11,617 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 theSigma (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 aMiller–Rabin primality test (3,174 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 (AugustGustav 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 electronsMathematical 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). ConvergenceJohn von Neumann (14,732 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 askedRiesz 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 aAutomatic 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 theoryEdgar 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, andLeon 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,Arithmetic 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). "LogarithmicJohn 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. McKayIreland (18,037 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 (5,837 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:Quaternion (10,179 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 1989Jean-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 nombresSPECfp (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 primalityList 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 JuliusFuzhou (5,909 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 ofExplicit formulae (L-function) (2,216 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-VerlagRoyal Medal (326 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 celebratedFeynman–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 andFourier 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, statisticsTimeline 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 introducesCryptography (8,581 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 ofBuckeye TV (2,135 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 receivedGolden ratio (10,422 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 978-0-521-85014-8Government Communications Headquarters (5,932 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 feasibleExpander 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, CambridgeÉmile 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)Heidelberg 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:Fibonacci 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: CambridgeDisjunctive 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: CambridgeContinued fraction (7,506 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 PerronATS 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 problemsBinary 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 applications3-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 theoryMatrix (mathematics) (11,999 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 physicsDamodar 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 ScientificCounter-Earth (2,930 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'Ricci 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 thatYoung Scientist and Technology Exhibition (940 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) FirstVolkenborn 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 276Pisot–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 1020University 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 BierstoneSobol 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 methodLee–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 (1,699 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 hypothesisIncompressibility method (3,606 words) [view diff] no match in snippet view article find links to article

expressed as binary strings in the sense of E. Borel; more in general the distribution of 0s and 1s in binary strings of high Kolmogorov complexity in. TheAncient 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. “TechniquesRomanovski 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 generalSavilian 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 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 measureElementary 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. ElementaryHistory of India (26,704 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 978-0-486-65620-5Ohio 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 groupLee 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; LCombinatorics on words (2,463 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: CambridgePythagorean 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 EarthList of Italian scientists (3,759 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 procedureScale relativity (10,595 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 slightArthur 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 manyHedonic 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 HausmanHerbert Scarf (9,703 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 rankedList of Italians (30,508 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 procedureLocalization (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 atheists in science and technology (29,065 words) [view diff] no match in snippet view article find links to article

British mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He is best known for theOscillator representation (21,545 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 functionsArtin 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-classMatematička 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