Dirichlet L-function for the Legendre symbol
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Definition
Suppose 
is a prime number. The Dirichlet L-function for the Legendred symbol mod is defined as the Dirichlet L-function for the Legendre symbol mod . In other words, it is the function given by the following L-series:
.
The numerator here is the Legendre symbol, which is 
if divides 
, 
if is a quadratic residue modulo , and 
if is a quadratic nonresidue modulo .
