A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively prime initial term and common difference contains infinitely many primes), modulo k is a complex function χ_k(n) for positive integer n such that χ_k(1) | = | 1 χ_k(n) | = | χ_k(n + k) χ_k(m) χ_k(n) | = | χ_k(m n) for all m, n, and χ_k(n) = 0

Dirichlet L-series | multiplicative character