Dirichlet L-function

Summary

A Dirichlet L-function is the Dirichlet series $L(s, \chi) = \sum_{n \ge 1} \chi(n) n^{-s}$ of a Dirichlet character $\chi$, together with its analytic continuation. It has an Euler product over the primes and generalizes the Riemann zeta function, which is the case of the trivial character modulo $1$. The fact that $L(1, \chi) \ne 0$ for every nonprincipal $\chi$ is the heart of Dirichlet's theorem on arithmetic progressions.