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searching for Distribution (number theory) 328 found (336 total)

alternate case: distribution (number theory)

Analytic number theory (3,575 words) [view diff] no match in snippet view article find links to article

fundamental differences in technique. Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of
Prime number theorem (5,738 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 formalizes
Smooth 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 by
Diophantine 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 Diophantus
Prime number (9,887 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 primes
List 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 hydrodynamics
Supersingular 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 over
Erdős–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,
Abstract 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 to
Random 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 eigenvalues
Totative (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) counts
Erdős 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 arcsine
Riemann zeta function (7,053 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 Logarithmic
Natural number (3,791 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, such
Riemann–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 the
P-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 numbers
Character 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. Cambridge
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 positive
Hilbert'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 concerned
Unusual 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 than
Prime 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 overlap
Square-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 978-1-4757-5194-9
Brun–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 prime
Vojta'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 diophantine
Bombieri–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, averaged
Skewes' 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 for
List 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; important
Elliott–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 applications
Cramér'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 consecutive
Cyclotomic 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)−1
Multiplicative 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 usually
Digit 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 of
Binomial 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 by
List 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–TIS
Hermann 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 zeta
Greek 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 microlitre
Carmichael 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 modular
Gaussian 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 addition
Gillies' 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 in
Schwartz–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–Bruhat
Pál 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 in
List 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 (probability
Elliptic 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 numbers
Bateman–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, named
Wolfgang 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 subspace
L-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-series
Quadratic 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 {\displaystyle
Riemann 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  Gourdon
Maier'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 numbers
Barban–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 1-56881-162-4
Goldbach's conjecture (2,755 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 2
List 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 connection
Champernowne 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.; Nicolas
SageMath (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 February
Dirichlet 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 primes
Stoneham 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 Mathematics
Effective 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 to
Prime-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 conjectured
Manin 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 number
Heath-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=X1X2X3
Chebotarev's density theorem (2,021 words) [view diff] no match in snippet view article find links to article
Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field
Illegal prime (592 words) [view diff] no match in snippet view article find links to article
prime is a prime number that represents information whose possession or distribution is forbidden in some legal jurisdiction. One of the first illegal primes
Bernhard 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 mostly
Primecoin (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 portal
Akshay 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 ergodic
Dirichlet'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, there
William J. LeVeque (591 words) [view diff] no match in snippet view article find links to article
was number theory, specifically transcendental numbers, uniform distribution, and Diophantine approximation. He wrote a number of number theory textbooks
Equidistributed 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 sequence
Harold 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 Accrington
Serge 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 Algebra
George 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 his
Kohji 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 for
Matsumoto 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,
Mikio 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 been
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-Universität
Harmonic 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 related
Firoozbakht'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 the
Leonhard Euler (7,040 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 and
Hecke 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 larger
Sinkov 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 combinatorics
Lists 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 and
Number (6,335 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 uses
Mellin 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; it
Pi (15,996 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, mechanics
Helge 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 hypothesis
Karl 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, Primzahlverteilung
List 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 Perturbation
Quadratic 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 integer
Mertens 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 M
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 started
Number 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 reviews
Helmut 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"
Normal distribution (18,346 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, which
E (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 probability
Discrete 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, particularly
Elliptic unit (354 words) [view diff] no match in snippet view article find links to article
prime p then Θa(Q) is a unit away from p. The function Θa satisfies a distribution relation for b = (β) coprime to a: Modular unit Coates, J.H.; Greenberg
Edmund 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 Berlin
Montgomery'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 Mathematical
Timeline 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 multiplication
List 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's
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 that
Yuri 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 in
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 extension
Graham 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 Mathematical
Euler'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 that
Chebyshev'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 the
Normal 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 1-56881-162-4
On 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 during
Maier'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 primes
Florian 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 functions
Euclidean algorithm (14,001 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 factorizations
Perfect totient number (594 words) [view diff] no match in snippet view article find links to article
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to
Divisor 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 asymptotic
Conjecture (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 theorists
Logarithm (10,692 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 theory
Timothy 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 to
Gumbel 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 integer
Peter Gustav Lejeune Dirichlet (3,194 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 and
Abc 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). It
Robert 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 later
Liouville 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:
Solomon 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 Tetris
Roth'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 type
Partition 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 theory
Regular 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 prove
Péter 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 achievements
Elementary 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 time
Rodion 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 1928
Gamma function (9,180 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 (represented
Basel 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 Euler
Tibor 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 undergraduate
Ramin 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 Theory
Pierre 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 the
Rational 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 the
Haar 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 theory
Pan 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 Shandong
Change-making problem (1,336 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 likewise
Ferdinand 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 generally
Electrical 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 electrical
Big O notation (6,908 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 between
Von 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, physics
Practical 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 sums
Mark 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 Nottingham
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. Baron
Regular (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 the
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 education
Legendre'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 (
Carl 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, geophysics
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 both
Fermat 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 theorem
Adrien-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 number
Paul 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 formulating
Poisson 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 functional
Hilbert–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 possible
Complex number (10,509 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 advantage
Nick 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 Princeton
Phi (1,144 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 functions
Harald 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. His
Glossary of areas of mathematics (5,623 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 other
List 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 Dirichlet
Problems 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 points
Jonas 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 term
Kolakoski 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: American
Klaus 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 birthday
Ilya 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 contribution
Euler–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 defined
Statistics (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 tools
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 . Grimmett
Prime gap (2,836 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 favourite
Transcendental 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 theory
Alexandru 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 known
Outline 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 forms
Ramanujan'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 Series
Beurling 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 prime
Vinogradov'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 numbers
Unit 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 conjecture
List 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. (This
S.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 an
Bernoulli 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 = ±1/2
Contributions 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. In
Refactorable 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 computer
William 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 University
Jacques 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 differential
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 translation
Zeta 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 function
Harald 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:
Hee 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 extensively
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 proposed
Sylvester 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 general
Fields Medal (2,445 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, US
Khinchin's constant (1,333 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 have
Twin prime (2,059 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, which
Gérald 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 and
Cousin 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) (7,348 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 exponentiation
Giuseppe 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-digit
Fourier 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 formula
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 different
Nevanlinna 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 tool
Theorem (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 proof
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 uses
Wallenius' 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 statictics
History of mathematics (12,479 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 order
Bell 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: Partition
Closed-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 encoding
Ergodic 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:
Kummer 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, again
1935 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 American
Noncentral 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 in
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, A
Mertens 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. Retrieved
Hurwitz 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 also
Henri Poincaré (8,634 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 theory
Liouville 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 with
Michał 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 relieve
Felix 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 biquadratic
Elliptic 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 Ed
1837 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 and
French 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; Charles
Ars 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 are
Ideal 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 place
List 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 of
Sigma (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 a
D. 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 the
Erdős–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 Mathematical
Hà 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 J
Pythagorean 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 . For
Feedback 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 integer
Carl-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. Esseen
Partition 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 integers
Golden ratio (10,442 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 978-0-521-85014-8
Complexity 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: Cambridge
Hardy–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, Michiel
Explicit formulae (L-function) (2,742 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-Verlag
List 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 1868–1942
Richard 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)90078-4
Number sign (3,514 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 file
The 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 1.2
Bc (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 particle
Polylogarithm (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 Colloquium
Naor–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–Reingold
Cryptography (8,583 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 of
Cryptography (8,583 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 of
Millennium 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 problem
Generalized 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 on
Neural 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 based
Freeman Dyson (7,972 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 Fellow
Diffie–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 2005-11-23
Lambda (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, intended
Mathematical 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 organizations
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 multiplication
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. Graduate
Differential equation (3,845 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 Control
Taylor'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 Mertens
Almost 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"
Alexander 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)
Miller–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 (August
John von Neumann (14,700 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 asked
Vector 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 the
Gustav 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 electrons
Thue–Morse sequence (2,957 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 was
Ulam spiral (1,877 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. (March
Erdős–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)80027-5
Edgar 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, and
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 theory
Leon Ehrenpreis (592 words) [view diff] no match in snippet view article find links to article
Mathematics Genealogy Project Grinberg, Eric L. (2000), Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis, American Mathematical Society,
Riesz mean (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 a
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). "Logarithmic
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.  McKay
Ireland (18,063 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 composite
History 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:
Quaternion (10,195 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 1989
Jean-Marie De Koninck (1,750 words) [view diff] no match in snippet view article find links to article
l'ingénieur, Éditions Loze, Montréal, 2004 1001 Problems in Classical Number Theory (with Armel Mercier), American Mathematical Society, 2007 Ces nombres
List 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 Julius
Fourier 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, statistics
SPECfp (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 primality
Fuzhou (5,877 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 of
Royal 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 celebrated
Chebyshev function (2,129 words) [view diff] no match in snippet view article find links to article
Theory of the Distribution of Primes", Acta Mathematica, 41 (1916) pp. 119–196. ^ Davenport, Harold (2000). In Multiplicative Number Theory. Springer. p
Feynman–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 and
Matrix (mathematics) (12,127 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 physics
Expander 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, Cambridge
Timeline 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 introduces
Buckeye TV (2,148 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 received
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)
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:
History of India (26,744 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 978-0-486-65620-5
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: Cambridge
Continued 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  Perron
Government 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 feasible
Disjunctive 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: Cambridge
Binary 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 applications
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 problems
Incompressibility 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 basic
3-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 theory
Damodar 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 Scientific
Counter-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 that
University 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 Bierstone
Volkenborn integral (610 words) [view diff] no match in snippet view article find links to article
p-adisches Integral und seine Anwendungen II. In: Manuscripta Mathematica. Bd. 12, Nr. 1, 1974, [2] Henri Cohen, "Number Theory", Volume II, page 276
Young Scientist and Technology Exhibition (951 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) First
Sobol 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 method
Pisot–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 1020
Mathematical 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). Convergence
Lee–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 Mathematical
Ancient 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. “Techniques
Andrew 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 hypothesis
Romanovski 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 general
Savilian 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 also
Quasi-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 measure
Elementary 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. Elementary
Ohio 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 group
Pythagorean 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 Earth
Lee 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; L
Combinatorics 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: Cambridge
List of Italian scientists (3,772 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 procedure
Scale 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 relativity
Hedonic 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 Hausman
Multiply-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 slight
Arthur 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 many
Herbert 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 ranked
List of Italians (30,528 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 procedure
Localization (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 (33,792 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 the
Oscillator 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 functions
Artin 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-class
Matematička 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