L functions and the oscillator representation / / Stephen Rallis

• Autore: Rallis Stephen <1942->
• Pubblicazione: Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1987]; ©1987
• Edizione: 1st ed. 1987.
• Descrizione fisica: 1 online resource (XVI, 240 p.)
• Disciplina: 512.7
• Soggetto topico: Representations of groups; Number theory
• Classificazione: 10D05
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: Notation and preliminaries -- Special Eisenstein series on orthogonal groups -- Siegel formula revisited -- Inner product formulae -- Siegel formula — Compact case -- Local l-factors -- Global theory.
• Sommario/riassunto: 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.
• Titolo autorizzato: L-functions and the oscillator representation
• ISBN: 3-540-47761-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466515403316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1245