Definition:Dirichlet L-function

Definition
Let $\chi : \left( \Z / q \Z \right)^\times \to \C^\times$ be a Dirichlet character.

A Dirichlet $L$-function is a Dirichlet series


 * $\displaystyle L(s,\chi) = \sum_{n \geq 1} \chi(n)n^{-s}$

for all $s \in \C$ such that the sum converges.

This is extended to the complex plane by Analytic Continuation of Dirichlet L-functions.