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 .