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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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

Funding Information:
The research of the second author was supported by the German University of Technology in Oman , by Research stays at the Max-Planck-Institute of Mathematics in Bonn in 2011 and 2013, and the Graduiertenkolleg Experimentelle und konstruktive Algebra at the RWTH Aachen.

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Automorphic L-functions
Degenerate principal series
Differential operators
Ikeda lifts

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10.1016/j.jnt.2014.01.030

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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.",

keywords = "Automorphic L-functions, Degenerate principal series, Differential operators, Ikeda lifts",

author = "Paul Garrett and Bernhard Heim",

note = "Funding Information: The research of the second author was supported by the German University of Technology in Oman , by Research stays at the Max-Planck-Institute of Mathematics in Bonn in 2011 and 2013, and the Graduiertenkolleg Experimentelle und konstruktive Algebra at the RWTH Aachen. Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

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doi = "10.1016/j.jnt.2014.01.030",

language = "English (US)",

volume = "146",

pages = "171--186",

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AU - Garrett, Paul

AU - Heim, Bernhard

N1 - Funding Information: The research of the second author was supported by the German University of Technology in Oman , by Research stays at the Max-Planck-Institute of Mathematics in Bonn in 2011 and 2013, and the Graduiertenkolleg Experimentelle und konstruktive Algebra at the RWTH Aachen. Publisher Copyright: © 2014 Elsevier Inc.

PY - 2015

Y1 - 2015

N2 - 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.

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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DO - 10.1016/j.jnt.2014.01.030

M3 - Article

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SN - 0022-314X

VL - 146

SP - 171

EP - 186

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - C

ER -

Hecke duality of Ikeda lifts

Abstract

Bibliographical note

Keywords

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