nLab Dirichlet character

Definition

e.g. Goldfeld-Hundley 11 (2.1.5) (2.1.6)

Properties

Relation to automorphic forms on the idele group

Dirichlet characters are essentially automorphic forms for the group of ideles in disguise. (Goldfeld-Hundley 11, theorem 2.1.9)

Related concepts

• Dirichlet theta function

• Dirichlet L-function

References

• Dorian Goldfeld, Joseph Hundley, chapter 2 of Automorphic representations and L-functions for the general linear group, Cambridge Studies in Advanced Mathematics 129, 2011 (pdf)