Dirichlet’s theorem on arithmetic progressions states that if a and k are coprime integers, then there are infinitely many prime numbers p such that p ≡ a (mod k). Amazingly, this statement can be reworked into a claim about Dirichlet L-series, which are complex-valued functions that are differentiable on their domains. Dirichlet’s theorem can be proven subsequently using methods from calculus and complex analysis.