Vipul: Created page with '==Definition== Suppose $p$ is a prime number. The '''Dirichlet L-function for the Legendred symbol''' mod $p$ is defined as the [[defining ingredient::...'

2009-05-07T13:51:23Z

Created page with '==Definition== Suppose <math>p</math> is a prime number. The '''Dirichlet L-function for the Legendred symbol''' mod <math>p</math> is defined as the [[defining ingredient::...'

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==Definition==

Suppose <math>p</math> is a [[prime number]]. The '''Dirichlet L-function for the Legendred symbol''' mod <math>p</math> is defined as the [[defining ingredient::Dirichlet L-function]] for the [[defining ingredient::Legendre symbol]] mod <math>p</math>. In other words, it is the function given by the following L-series:

<math>\sum_{n \in \mathbb{N}} \frac{\left(\frac{n}{p}\right)}{n^s}</math>.

The numerator here is the Legendre symbol, which is <math>0</math> if <math>p</math> divides <math>n</math>, <math>1</math> if <math>n</math> is a [[quadratic residue]] modulo <math>p</math>, and <math>-1</math> if <math>n</math> is a [[quadratic nonresidue]] modulo <math>p</math>.

Dirichlet L-function for the Legendre symbol - Revision history

Vipul: Created page with '==Definition== Suppose p is a prime number. The '''Dirichlet L-function for the Legendred symbol''' mod p is defined as the [[defining ingredient::...'

Vipul: Created page with '==Definition== Suppose $p$ is a prime number. The '''Dirichlet L-function for the Legendred symbol''' mod $p$ is defined as the [[defining ingredient::...'