This term is related to: Galois theory
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This article defines a type of L-function
This article or section of article is sourced from:Wikipedia
The Artin L-function associated with , denoted as , is defined as follows: it is the product, over all prime ideals , of the following Euler factor corresponding to that :
evaluated at .
Strictly speaking, the above definition works when is unramified. A slight variant works when is ramified.PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
For Abelian Galois group
When the underlying Galois group is Abelian, the Artin L-function specializes to the Hecke L-function.
For Abelian Galois group and over rationals
When is Abelian and , the Artin L-function specializes to the Dirichlet L-function.