Dirichlet's Theorem

Def Dirichlet L-function The Dirichlet -function is of the form: where is a Dirichlet character and a complex variable with real part greater than .

Lemma Fix . If , then Proof

Lemma Suppose , then we have Proof

Dirichlet's Theorem

For coprime positive integers , there are infinitely many primes that are congruent to modulo .

Proof