Definition:Dirichlet L-function

Definition

Let $q \in \Z_{>1}$ be a strictly positive integer.

Let $\chi : \Z \to \C$ be a Dirichlet character modulo $q$.

A Dirichlet $L$-function (associated to $\chi$) is a Dirichlet series:

$\ds \map L {s, \chi} = \sum_{n \mathop \ge 1} \map \chi n n^{-s}$

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

Also see

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

Source of Name

This entry was named for Johann Peter Gustav Lejeune Dirichlet.