Dirichlet characters

A Dirichlet character is a special kind of function used in number theory that assigns complex numbers to integers, with two main properties: it repeats values periodically based on a fixed modulus, and it’s zero whenever the integer shares a common factor with that modulus. These functions help mathematicians analyze properties of numbers in different mathematical systems, especially in studying prime numbers within certain arithmetic progressions. Think of them as tools that capture symmetry and structure in numbers, allowing deeper insights into patterns and distributions in number theory.