Dirichlet L-function for the Legendre symbol

Definition

Suppose $p$ is a prime number. The Dirichlet L-function for the Legendred symbol mod $p$ is defined as the Dirichlet L-function for the Legendre symbol mod $p$. In other words, it is the function given by the following L-series:

$\sum _{n\in \mathbb {N} }{\frac {\left({\frac {n}{p}}\right)}{n^{s}}}$.

The numerator here is the Legendre symbol, which is $0$ if $p$ divides $n$, $1$ if $n$ is a quadratic residue modulo $p$, and $-1$ if $n$ is a quadratic nonresidue modulo $p$.