L-Functions and the Oscillator Representation (Lecture Notes in Mathematics)

Stephen Rallis

ISBN 10: 0387176942 / ISBN 13: 9780387176949

Published by Springer Verlag, 1987

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Bibliographic Details

• Title: L-Functions and the Oscillator Representation (Lecture Notes in Mathematics)
• Publisher: Springer Verlag
• Publication Date: 1987
• Language: English
• ISBN 10: 0387176942
• ISBN 13: 9780387176949
• Binding: paperback
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

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Synopsis

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