On (χ,b)-factors of cuspidal automorphic representations of unitary groups I

Dihua Jiang; Chenyan Wu

doi:10.1016/j.jnt.2014.12.003

On (χ,b)-factors of cuspidal automorphic representations of unitary groups I

Dihua Jiang, Chenyan Wu

School of Mathematics

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

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Abstract

Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations σ of unitary groups and investigate their relation with the occurrence of a simple global Arthur parameter (χ, b) in the global Arthur parameter ψ_σ associated to σ, by the endoscopic classification of Arthur [Art13,Mok13,KMSW14]. The argument uses the theory of theta correspondence. This can be viewed as a part of the (χ, b)-theory outlined in [Jia14] and can be regarded as a refinement of the theory of theta correspondences and poles of certain L-functions, which was outlined in [Ral91].

Original language	English (US)
Pages (from-to)	88-118
Number of pages	31
Journal	Journal of Number Theory
Volume	161
DOIs	https://doi.org/10.1016/j.jnt.2014.12.003
State	Published - 2016

Bibliographical note

Funding Information:
The research of the first named author is supported in part by the NSF Grant DMS-1301567 .

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Arthur parameters
Poles of automorphic L-functions
Theta correspondence and periods

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10.1016/j.jnt.2014.12.003

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title = "On (χ,b)-factors of cuspidal automorphic representations of unitary groups I",

abstract = "Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations σ of unitary groups and investigate their relation with the occurrence of a simple global Arthur parameter (χ, b) in the global Arthur parameter ψσ associated to σ, by the endoscopic classification of Arthur [Art13,Mok13,KMSW14]. The argument uses the theory of theta correspondence. This can be viewed as a part of the (χ, b)-theory outlined in [Jia14] and can be regarded as a refinement of the theory of theta correspondences and poles of certain L-functions, which was outlined in [Ral91].",

keywords = "Arthur parameters, Poles of automorphic L-functions, Theta correspondence and periods",

author = "Dihua Jiang and Chenyan Wu",

note = "Funding Information: The research of the first named author is supported in part by the NSF Grant DMS-1301567 . Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2016",

doi = "10.1016/j.jnt.2014.12.003",

language = "English (US)",

volume = "161",

pages = "88--118",

journal = "Journal of Number Theory",

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TY - JOUR

T1 - On (χ,b)-factors of cuspidal automorphic representations of unitary groups I

AU - Jiang, Dihua

AU - Wu, Chenyan

PY - 2016

Y1 - 2016

N2 - Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations σ of unitary groups and investigate their relation with the occurrence of a simple global Arthur parameter (χ, b) in the global Arthur parameter ψσ associated to σ, by the endoscopic classification of Arthur [Art13,Mok13,KMSW14]. The argument uses the theory of theta correspondence. This can be viewed as a part of the (χ, b)-theory outlined in [Jia14] and can be regarded as a refinement of the theory of theta correspondences and poles of certain L-functions, which was outlined in [Ral91].

AB - Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations σ of unitary groups and investigate their relation with the occurrence of a simple global Arthur parameter (χ, b) in the global Arthur parameter ψσ associated to σ, by the endoscopic classification of Arthur [Art13,Mok13,KMSW14]. The argument uses the theory of theta correspondence. This can be viewed as a part of the (χ, b)-theory outlined in [Jia14] and can be regarded as a refinement of the theory of theta correspondences and poles of certain L-functions, which was outlined in [Ral91].

KW - Arthur parameters

KW - Poles of automorphic L-functions

KW - Theta correspondence and periods

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DO - 10.1016/j.jnt.2014.12.003

M3 - Article

AN - SCOPUS:84963642426

VL - 161

SP - 88

EP - 118

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

On (χ,b)-factors of cuspidal automorphic representations of unitary groups I

Abstract

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