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References for Chapter II
Automorphic forms are discussed in terms of group representations in [3] and [11] as well as
Godement, R., Analyse spectrale des fonctions modulaires, Seminaire Bourbaki, No. 278.
Godement, R., Introduction à la theorie de Langlands, Seminaire Bourbaki, No. 321.
As its name implies the Hecke theory is a creation of Hecke.
Hecke, E., Mathematische Werke.
Maass seems to have been the first to consider it outside the classical context.
Maass, H., Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktiongleichungen, Math. Ann., 121 (1944).
It seems to have been Weil who first used several L-functions to prove a converse theorem.
Weil, A., Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168 (1967).
His generalizations of the Artin L-functions are introduced in
Weil, A., Sur la théorie du corps de classes, Jour. Math. Soc. Japan, vol. 3 (1951).
For various technical facts used in the twelfth paragraph we refer to
langlands, R., On the functional equation of the Artin L-functions, Notes, Yale University (in preparation).
We have also had occasion to refer to
Chevalley, C., Deux théorèmes d'arithmetique, Jour. Math. Soc. Japan, vol. 3 (1951).
A result more or less the same as Proposition 12.1 is proved in
Shalika, J.A and S. Tanaka, On an explicit construction of a certain class of automorphic forms, Preprint.
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Jacquet, H., Langlands, R.P. (1970). Global Theory. In: Automorphic Forms on GL (2). Lecture Notes in Mathematics, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058990
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DOI: https://doi.org/10.1007/BFb0058990
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