Dirichlet character

A Dirichlet character is a mathematical function used in number theory that assigns complex numbers to integers in a structured way. It is periodic, meaning its value repeats every certain number (called the modulus), and it outputs zero for numbers that share factors with that modulus. For numbers coprime with the modulus, it outputs values on the unit circle in the complex plane, following specific multiplicative rules. These functions help analyze properties of prime numbers within arithmetic sequences and are key components in understanding advanced concepts like Dirichlet's theorem on primes in arithmetic progressions.