Number theory/Related Articles

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A list of Citizendium articles, and planned articles, about Number theory.
See also changes related to Number theory, or pages that link to Number theory or to this page or whose text contains "Number theory".

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  • Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields. [e]
  • Algebraic number field [r]: A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory. [e]
  • Algebraic number [r]: A complex number that is a root of a polynomial with rational coefficients. [e]
  • Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity. [e]
  • Arithmetic function [r]: A function defined on the set of positive integers, usually with integer, real or complex values, studied in number theory. [e]
  • Artin L-function [r]: A type of Dirichlet series associated to a linear representation ρ of a Galois group G. [e]
  • Asymmetric key cryptography [r]: A category of cryptographic techniques, which greatly simplify key management, which are based on mathematically related key pairs, such that the "public" key can be used to encrypt and be freely available, and only the holder of the "private" key can decrypt the message [e]
  • Average order of an arithmetic function [r]: A simple or well-known function, usually continuous and montonic, which on average takes the same or closely approximate values as a given arithmetic function. [e]
  • Basel problem [r]: The problem of finding the sum of the infinite series 1 + 1/4 + 1/9 + 1/16 + 1/25 + ···. [e]
  • Bernhard Riemann [r]: German mathematician (1826-1866) notable for differential geometry, function theory, and number theory. [e]
  • Calculus [r]: The elementary study of real (or complex) functions involving derivatives and integration. [e]
  • Carl Friedrich Gauss [r]: German mathematician, who was one of the most influential figures in the history of mathematics and mathematical physics (1777 – 1855). [e]
  • Catalog of special functions [r]: Add brief definition or description
  • Chinese remainder theorem [r]: Theorem that if the integers m1, m2, …, mn are relatively prime in pairs and if b1, b2, …, bn are integers, then there exists an integer that is congruent to bi modulo mi for i=1,2, …, n. [e]
  • Combinatorics [r]: Branch of mathematics concerning itself, at the elementary level, with counting things. [e]
  • Complex analysis [r]: Field of mathematics, precisely of mathematical analysis, that studies those properties which characterize functions of complex variables. [e]
  • Cryptography [r]: A field at the intersection of mathematics and computer science that is concerned with the security of information, typically the confidentiality, integrity and authenticity of some message. [e]
  • Dedekind zeta function [r]: Generalization of the Riemann zeta function to algebraic number fields. [e]
  • Diophantine equation [r]: Equation in which the unknowns are required to be integers. [e]
  • Dirichlet character [r]: A group homomorphism on the multiplicative group in modular arithmetic extended to a multiplicative function on the positive integers. [e]
  • Dirichlet series [r]: An infinite series whose terms involve successive positive integers raised to powers of a variable, typically with integer, real or complex coefficients. [e]
  • Discrete mathematics [r]: The disciplines within mathematics that study discrete objects: combinatorics, graph theory, number theory, mathematical logic, … [e]
  • Egypt [r]: A country in the northeastern corner of Africa, bordering Sudan, Libya, the Mediterranean Sea and the Red Sea [e]
  • Ernst Eduard Kummer [r]: (29 January 1810 - 14 May 1893) German mathematician who codified some of the relations between different hypergeometric series, proved Fermat's last theorem for a considerable class of prime exponents, and found the Kummer surface. [e]
  • Euclid's lemma [r]: A prime number that divides a product of two integers must divide one of the two integers. [e]
  • Euclidean algorithm [r]: Algorithm for finding the greatest common divisor of two integers [e]
  • Euclid [r]: (ca. 325 BC - ca. 265 BC) Alexandrian mathematician and known as the father of geometry. [e]
  • Fibonacci number [r]: Element of the sequence in which the first number is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers. [e]
  • Gamma function [r]: A mathematical function that extends the domain of factorials to non-integers. [e]
  • Generating function [r]: Function g(x,y) corresponding to a family of orthogonal polynomials ƒ0(x), ƒ1(x),…, where a Taylor series expansion of g(x,y) in powers of y will have the polynomial ƒn (x) as the coefficient for the term yn. [e]
  • Goldbach's conjecture [r]: Unestablished conjecture that every even number except the number 2 is the sum of two primes. [e]
  • Graph theory [r]: Field of mathematics studying graphs, which consist of nodes and arcs joining the nodes. [e]
  • Green's function [r]: Auxiliary function in the theory of linear differential equations; integral operator with Green function as kernel is the inverse of a linear differential operator. [e]
  • Group theory [r]: Branch of mathematics concerned with groups and the description of their properties. [e]
  • International Mathematical Olympiad [r]: Annual mathematics contest for high school students from across the world. [e]
  • Jordan's totient function [r]: A generalisation of Euler's totient function. [e]
  • Lambda function [r]: The exponent of the multiplicative group modulo an integer. [e]
  • Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]
  • Modular arithmetic [r]: Form of arithmetic dealing with integers in which all numbers having the same remainder when divided by a whole number are considered equivalent. [e]
  • Möbius function [r]: Arithmetic function which takes the values -1, 0 or +1 depending on the prime factorisation of its input n. [e]
  • Natural number [r]: An element of 1, 2, 3, 4, ..., often also including 0. [e]
  • Normal distribution [r]: a symmetrical bell-shaped probability distribution representing the frequency of random variations of a quantity from its mean. [e]
  • Normal order of an arithmetic function [r]: A simple or well-known function, usually continuous and montonic, which "usually" takes the same or closely approximate values as a given arithmetic function. [e]
  • Number Theory Foundation [r]: A non-profit organisation based in the United States which supports research and conferences in the field of number theory. [e]
  • Number of divisors function [r]: The number of positive integer divisors of a given number. [e]
  • Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring. [e]
  • Oxford University Press [r]: Major international publisher of scholarly books, journals and reference works. [e]
  • P-adic metric [r]: A metric on the rationals in which numbers are close to zero if they are divisible by a large power of a given prime p. [e]
  • Partition (mathematics) [r]: Concepts in mathematics which refer either to a partition of a set or an ordered partition of a set, or a partition of an integer, or a partition of an interval. [e]
  • Partition function (number theory) [r]: The number of additive partitions of a positive integer. [e]
  • Prime number [r]: A number that can be evenly divided by exactly two positive whole numbers, namely one and itself. [e]
  • Primitive root [r]: A generator of the multiplicative group in modular arithmetic when that group is cyclic. [e]
  • Riemann zeta function [r]: Mathematical function of a complex variable important in number theory for its connection with the distribution of prime numbers. [e]
  • Riemann-Hurwitz formula [r]: Formula which describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. [e]
  • Riemann [r]: Add brief definition or description
  • Science [r]: The organized body of knowledge based on non–trivial refutable concepts that can be verified or rejected on the base of observation and experimentation [e]
  • Selberg sieve [r]: A technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. [e]
  • Serge Lang [r]: (19 May 1927 – 12 September 2005) French-born American mathematician known for his work in number theory and for his mathematics textbooks, including the influential Algebra. [e]
  • Sum-of-divisors function [r]: The function whose value is the sum of all positive divisors of a given positive integer. [e]
  • Szpiro's conjecture [r]: A relationship between the conductor and the discriminant of an elliptic curve. [e]
  • Totient function [r]: The number of integers less than or equal to and coprime to a given integer. [e]
  • Turan sieve [r]: A technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. [e]
  • Wilhelm Eduard Weber [r]: (Wittenberg October 24, 1804 – Göttingen June 23, 1891) German physicist known for his work in magnetism and on electromagnetic units. [e]
  • Zeta function [r]: Add brief definition or description