L-Functions and the Oscillator Representation (Paperback, 1987 ed.)

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

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 1245
Release date:	March 1987
First published:	1987
Authors:	Stephen Rallis
Dimensions:	235 x 155 x 13mm (L x W x T)
Format:	Paperback
Pages:	240
Edition:	1987 ed.
ISBN-13:	978-3-540-17694-7
Categories:	Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	3-540-17694-2
Barcode:	9783540176947

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