Representation Theory
Dirichlet characters are specific types of characters used in number theory that arise in the context of Dirichlet L-functions. These characters are completely multiplicative functions defined on the integers modulo some positive integer, providing a way to generalize the notion of characters from groups to the setting of algebraic number theory. They play a crucial role in understanding the distribution of prime numbers in arithmetic progressions and are instrumental in proving Dirichlet's theorem on primes in arithmetic progressions.
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