L-Functions and the Oscillator Representation

Stephen Rallis (Autor)

Buch | Softcover

XVI, 240 Seiten

1987
Springer Berlin (Verlag)
978-3-540-17694-7 (ISBN)

Infos

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

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 25.3.1987
• Reihe/Serie: Lecture Notes in Mathematics
• Zusatzinfo: XVI, 240 p.
• Verlagsort: Berlin
• Sprache: englisch
• Maße: 155 x 235 mm
• Gewicht: 363 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: automorphic forms • Lie group • Representation Theory
• ISBN-10: 3-540-17694-2 / 3540176942
• ISBN-13: 978-3-540-17694-7 / 9783540176947
• Zustand: Neuware