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L-Functions and the Oscillator Representation by Stephen Rallis
L-Functions and the Oscillator Representation by Stephen Rallis
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L-Functions and the Oscillator Representation

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Description

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
Release date NZ
March 25th, 1987
Audiences
  • Postgraduate, Research & Scholarly
  • Professional & Vocational
  • Undergraduate
Illustrations
XVI, 240 p.
Pages
240
Dimensions
156x234x13
ISBN-13
9783540176947
Product ID
2826639

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