Stephen Rallis

L-Functions and the Oscillator Representation

• Broschiertes Buch

Produktbeschreibung

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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Produktdetails

• Lecture Notes in Mathematics 1245
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-17694-7
• 1987.
• Seitenzahl: 256
• Erscheinungstermin: 25. März 1987
• Englisch
• Abmessung: 235mm x 155mm x 15mm
• Gewicht: 418g
• ISBN-13: 9783540176947
• ISBN-10: 3540176942
• Artikelnr.: 23844155

Inhaltsangabe

Notation and preliminaries.- Special Eisenstein series on orthogonal groups.- Siegel formula revisited.- Inner product formulae.- Siegel formula - Compact case.- Local l-factors.- Global theory.