L-functions and the oscillator representation
Author(s)
Bibliographic Information
L-functions and the oscillator representation
（Lecture notes in mathematics, 1245）
Springer-Verlag, c1987
- : gw
- : us
Available at 66 libraries
Note
Bibliography: p. [237]-238
Includes index
Description and Table of Contents
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
Table of Contents
Notation and preliminaries.- Special Eisenstein series on orthogonal groups.- Siegel formula revisited.- Inner product formulae.- Siegel formula - Compact case.- Local l-factors.- Global theory.
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