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].
Original language | English (US) |
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Pages (from-to) | 88-118 |
Number of pages | 31 |
Journal | Journal of Number Theory |
Volume | 161 |
DOIs | |
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