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

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

- 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)

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