Definition:Dirichlet L-function
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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.