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＜電子ブック＞
L-Functions and the Oscillator Representation / by Stephen Rallis
(Lecture Notes in Mathematics. ISSN:16179692 ; 1245)

版	1st ed. 1987.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1987
大きさ	XVI, 240 p : online resource
著者標目	*Rallis, Stephen author SpringerLink (Online service)
件　名	LCSH:Number theory FREE:Number Theory
一般注記	Notation and preliminaries -- Special Eisenstein series on orthogonal groups -- Siegel formula revisited -- Inner product formulae -- Siegel formula — Compact case -- Local l-factors -- Global theory 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 HTTP:URL=https://doi.org/10.1007/BFb0077894

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