Global Theory

  • H. Jacquet
  • R. P. Langlands
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. 13.
    Godement, R., Analyse spectrale des fonctions modulaires, Seminaire Bourbaki, No. 278.Google Scholar
  2. 14.
    Godement, R., Introduction à la theorie de Langlands, Seminaire Bourbaki, No. 321.Google Scholar

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

  1. 15.
    Hecke, E., Mathematische Werke.Google Scholar

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

  1. 16.
    Maass, H., Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktiongleichungen, Math. Ann., 121 (1944).Google Scholar

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

  1. 17.
    Weil, A., Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168 (1967).Google Scholar

His generalizations of the Artin L-functions are introduced in

  1. 18.
    Weil, A., Sur la théorie du corps de classes, Jour. Math. Soc. Japan, vol. 3 (1951).Google Scholar

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

  1. 19.
    langlands, R., On the functional equation of the Artin L-functions, Notes, Yale University (in preparation).Google Scholar

We have also had occasion to refer to

  1. 20.
    Chevalley, C., Deux théorèmes d'arithmetique, Jour. Math. Soc. Japan, vol. 3 (1951).Google Scholar

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

  1. 21.
    Shalika, J.A and S. Tanaka, On an explicit construction of a certain class of automorphic forms, Preprint.Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • H. Jacquet
  • R. P. Langlands

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