L-Functions and the Oscillator Representation [electronic resource] /
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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Format: | Texto biblioteca |
Language: | eng |
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Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
1987
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Subjects: | Mathematics., Number theory., Number Theory., |
Online Access: | http://dx.doi.org/10.1007/BFb0077894 |
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KOHA-OAI-TEST:1884362018-07-30T23:11:51ZL-Functions and the Oscillator Representation [electronic resource] / Rallis, Stephen. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,1987.engThese 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.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.Mathematics.Number theory.Mathematics.Number Theory.Springer eBookshttp://dx.doi.org/10.1007/BFb0077894URN:ISBN:9783540477617 |
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Mathematics. Number theory. Mathematics. Number Theory. Mathematics. Number theory. Mathematics. Number Theory. Rallis, Stephen. author. SpringerLink (Online service) L-Functions and the Oscillator Representation [electronic resource] / |
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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. |
format |
Texto |
topic_facet |
Mathematics. Number theory. Mathematics. Number Theory. |
author |
Rallis, Stephen. author. SpringerLink (Online service) |
author_facet |
Rallis, Stephen. author. SpringerLink (Online service) |
author_sort |
Rallis, Stephen. author. |
title |
L-Functions and the Oscillator Representation [electronic resource] / |
title_short |
L-Functions and the Oscillator Representation [electronic resource] / |
title_full |
L-Functions and the Oscillator Representation [electronic resource] / |
title_fullStr |
L-Functions and the Oscillator Representation [electronic resource] / |
title_full_unstemmed |
L-Functions and the Oscillator Representation [electronic resource] / |
title_sort |
l-functions and the oscillator representation [electronic resource] / |
publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
publishDate |
1987 |
url |
http://dx.doi.org/10.1007/BFb0077894 |
work_keys_str_mv |
AT rallisstephenauthor lfunctionsandtheoscillatorrepresentationelectronicresource AT springerlinkonlineservice lfunctionsandtheoscillatorrepresentationelectronicresource |
_version_ |
1756265783813472256 |