L-Functions and the Oscillator Representation

  • Authors
  • Stephen Rallis

Part of the Lecture Notes in Mathematics book series (LNM, volume 1245)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Stephen Rallis
    Pages 1-9
  3. Stephen Rallis
    Pages 25-48
  4. Stephen Rallis
    Pages 49-86
  5. Stephen Rallis
    Pages 87-127
  6. Stephen Rallis
    Pages 128-173
  7. Stephen Rallis
    Pages 174-199
  8. Back Matter
    Pages 200-239

About this book

Introduction

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

Keywords

automorphic forms lie group representation theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0077894
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17694-7
  • Online ISBN 978-3-540-47761-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book