Dirichlet L-function

From Number
Jump to: navigation, search

Definition

A Dirichlet L-function is a meromorphic function obtained as the analytic continuation of the Dirichlet series of the Dirichlet character.

The corresponding Dirichlet series is termed a Dirichlet L-series, and the Dirichlet L-series as well as the function are denoted where is the character and is the argument.

,

where is the set of all prime numbers. The equality follows from the Euler product formula.