E-Book, Englisch, Band 1245, 240 Seiten, eBook
Reihe: Lecture Notes in Mathematics
Rallis L-Functions and the Oscillator Representation
Erscheinungsjahr 2006
ISBN: 978-3-540-47761-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 1245, 240 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-47761-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
Notation and preliminaries.- Special Eisenstein series on orthogonal groups.- Siegel formula revisited.- Inner product formulae.- Siegel formula — Compact case.- Local l-factors.- Global theory.
