L-Functions and the Oscillator Representation by Stephen RallisL-Functions and the Oscillator Representation by Stephen Rallis

L-Functions and the Oscillator Representation

byStephen Rallis

Paperback | March 25, 1987

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These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N
Title:L-Functions and the Oscillator RepresentationFormat:PaperbackDimensions:254 pagesPublished:March 25, 1987Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540176942

ISBN - 13:9783540176947

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Table of Contents

Notation and preliminaries.- Special Eisenstein series on orthogonal groups.- Siegel formula revisited.- Inner product formulae.- Siegel formula - Compact case.- Local l-factors.- Global theory.