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
| Autorius: | Stephen Rallis |
| Serija: | Lecture Notes in Mathematics |
| Leidėjas: | Springer Berlin Heidelberg |
| Išleidimo metai: | 1987 |
| Knygos puslapių skaičius: | 256 |
| ISBN-10: | 3540176942 |
| ISBN-13: | 9783540176947 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Number theory |
Parašykite atsiliepimą apie „L-Functions and the Oscillator Representation“
