L-Functions and the Oscillator Representation

By Stephen Rallis

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

• Format: Paperback
• Language: English
• ISBN: 3540176942
• ISBN13: 9783540176947
• Release Date: March 1987
• Publisher: Springer
• Length: 240 Pages
• Weight: 0.80 lbs.
• Dimensions: 0.5" x 6.1" x 9.2"