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Global Theory

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Part of the Lecture Notes in Mathematics book series (LNM,volume 114)

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References for Chapter II

Automorphic forms are discussed in terms of group representations in [3] and [11] as well as

  1. Godement, R., Analyse spectrale des fonctions modulaires, Seminaire Bourbaki, No. 278.

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  2. Godement, R., Introduction à la theorie de Langlands, Seminaire Bourbaki, No. 321.

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As its name implies the Hecke theory is a creation of Hecke.

  1. Hecke, E., Mathematische Werke.

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Maass seems to have been the first to consider it outside the classical context.

  1. Maass, H., Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktiongleichungen, Math. Ann., 121 (1944).

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It seems to have been Weil who first used several L-functions to prove a converse theorem.

  1. Weil, A., Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168 (1967).

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His generalizations of the Artin L-functions are introduced in

  1. Weil, A., Sur la théorie du corps de classes, Jour. Math. Soc. Japan, vol. 3 (1951).

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For various technical facts used in the twelfth paragraph we refer to

  1. langlands, R., On the functional equation of the Artin L-functions, Notes, Yale University (in preparation).

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We have also had occasion to refer to

  1. Chevalley, C., Deux théorèmes d'arithmetique, Jour. Math. Soc. Japan, vol. 3 (1951).

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A result more or less the same as Proposition 12.1 is proved in

  1. Shalika, J.A and S. Tanaka, On an explicit construction of a certain class of automorphic forms, Preprint.

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© 1970 Springer-Verlag

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04903-6

  • Online ISBN: 978-3-540-36234-0

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