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L-Functions and the Oscillator Representation

  • Book
  • © 1987

Overview

Authors:
  1. Stephen Rallis

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

  • 4296 Accesses

  • 42 Citations

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About this book

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Notation and preliminaries

    • Stephen Rallis
    Pages 1-9

  3. Special Eisenstein series on orthogonal groups

    • Stephen Rallis
    Pages 10-24

  4. Siegel formula revisited

    • Stephen Rallis
    Pages 25-48

  5. Inner product formulae

    • Stephen Rallis
    Pages 49-86

  6. Siegel formula — Compact case

    • Stephen Rallis
    Pages 87-127

  7. Local l-factors

    • Stephen Rallis
    Pages 128-173

  8. Global theory

    • Stephen Rallis
    Pages 174-199

  9. Back Matter

    Pages 200-239
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Bibliographic Information

  • Book Title: L-Functions and the Oscillator Representation

  • Authors: Stephen Rallis

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0077894

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-17694-7Published: 25 March 1987

  • eBook ISBN: 978-3-540-47761-7Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 240

  • Topics: Number Theory

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