On the Functional Equations Satisfied by Eisenstein Series

Robert P. Langlands (auth.)9780387078724, 0-387-07872-X

Introduction.- Statement of assumptions. Some properties of discrete groups satisfying the assumptions.- Definition of a cusp form (after Gelfand). Basic properties of cusp forms.- Definition of Eisenstein series. Investigation of the constant term in the Fourier expansion of an Eisenstein series. A variant of a formula of Selberg.- Some lemmas used in Sections 6 and 7.- Proof of the function equations for the Eisenstein series associated to cusp forms.- Proof of the functional equations for all Eisenstein series. Statement of theorem.- References.- Appendices

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Table of contents :
Introduction….Pages 1-2
The assumptions….Pages 3-36
Cusp forms….Pages 37-60
Eisenstein series….Pages 61-99
Miscellaneous lemmas….Pages 100-118
Some functional equations….Pages 119-160
The main theorem….Pages 161-233