L-Functions and the Oscillator Representation (Lecture Notes in Mathematics, 1245)

Rallis, Stephen

ISBN 10: 3540176942 / ISBN 13: 9783540176947

Published by Springer, 1987

About this Item

Seller Inventory # E-9783540176947-2-2

Bibliographic Details

• Title: L-Functions and the Oscillator Representation (Lecture Notes in Mathematics, 1245)
• Publisher: Springer
• Publication Date: 1987
• Language: English
• ISBN 10: 3540176942
• ISBN 13: 9783540176947
• Binding: Soft cover
• Condition: Very good

About this title

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