Dirichlet L-function for the Legendre symbol

From Number
Revision as of 13:51, 7 May 2009 by Vipul (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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 .