18 relations: Arithmetic function, Coprime integers, Dirichlet character, Dirichlet convolution, Dirichlet L-function, Dirichlet series, Divisor function, Domain of a function, Fundamental theorem of arithmetic, Hadamard product (matrices), Jacobi symbol, Legendre symbol, Liouville function, Möbius function, Monomial, Multiplicative function, Natural number, Number theory.
In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers.
In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.
In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of \mathbb Z / k \mathbb Z. Dirichlet characters are used to define Dirichlet ''L''-functions, which are meromorphic functions with a variety of interesting analytic properties.
In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory.
In mathematics, a Dirichlet L-series is a function of the form Here χ is a Dirichlet character and s a complex variable with real part greater than 1.
In mathematics, a Dirichlet series is any series of the form where s is complex, and a_n is a complex sequence.
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.
In mathematics, the Hadamard product (also known as the Schur product or the entrywise product) is a binary operation that takes two matrices of the same dimensions, and produces another matrix where each element i,j is the product of elements i,j of the original two matrices.
Jacobi symbol for various k (along top) and n (along left side).
The Liouville function, denoted by λ(n) and named after Joseph Liouville, is an important function in number theory.
The classical Möbius function is an important multiplicative function in number theory and combinatorics.
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1).
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.