Hecke duality of Ikeda lifts

Paul Garrett; Bernhard Heim

doi:10.1016/j.jnt.2014.01.030

Hecke duality of Ikeda lifts

Paul Garrett, Bernhard Heim

Mathematics

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Abstract

Ikeda lifts form a distinguished subspace of Siegel modular forms. In this paper we prove several global and local results concerning this space. We find that degenerate principal series representations (for the Siegel parabolic) of the symplectic group Sp_2n of even degree satisfy a Hecke duality relation which has applications to Ikeda lifts and leads to converse theorems. Moreover we apply certain differential operators to study pullbacks of Ikeda lifts.

Original language	English (US)
Pages (from-to)	171-186
Number of pages	16
Journal	Journal of Number Theory
Volume	146
Issue number	C
DOIs	https://doi.org/10.1016/j.jnt.2014.01.030
State	Published - 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Automorphic L-functions
Degenerate principal series
Differential operators
Ikeda lifts

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title = "Hecke duality of Ikeda lifts",

abstract = "Ikeda lifts form a distinguished subspace of Siegel modular forms. In this paper we prove several global and local results concerning this space. We find that degenerate principal series representations (for the Siegel parabolic) of the symplectic group Sp2n of even degree satisfy a Hecke duality relation which has applications to Ikeda lifts and leads to converse theorems. Moreover we apply certain differential operators to study pullbacks of Ikeda lifts.",

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AU - Garrett, Paul

AU - Heim, Bernhard

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AB - Ikeda lifts form a distinguished subspace of Siegel modular forms. In this paper we prove several global and local results concerning this space. We find that degenerate principal series representations (for the Siegel parabolic) of the symplectic group Sp2n of even degree satisfy a Hecke duality relation which has applications to Ikeda lifts and leads to converse theorems. Moreover we apply certain differential operators to study pullbacks of Ikeda lifts.

KW - Automorphic L-functions

KW - Degenerate principal series

KW - Differential operators

KW - Ikeda lifts

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ER -

Hecke duality of Ikeda lifts

Abstract

Bibliographical note

Keywords

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