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L-Functions and the Oscillator Representation 9.0%OFF

L-Functions and the Oscillator Representation

by Stephen Rallis

  • ISBN

    :  

    9783540176947

  • Publisher

    :  

    Springer

  • Subject

    :  

    Mathematics

  • Binding

    :  

    Paperback

  • Pages

    :  

    254

  • Year

    :  

    505

₹

5117.0

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₹

4656.0

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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

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