Periods and (χ, b)-factors of cuspidal automorphic forms of symplectic groups

Dihua Jiang, Chenyan Wu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations σ of symplectic groups Sp2n(A), which detects the right-most pole of the L-function L(s, σ × χ) for some character χ of F×A × of order at most 2, and hence the occurrence of a simple global Arthur parameter (χ, b) in the global Arthur parameter ψ attached to σ. We also give a characterisation of first occurrences of theta correspondence by (regularised) period integrals of residues of certain Eisenstein series.

Original languageEnglish (US)
Pages (from-to)267-320
Number of pages54
JournalIsrael Journal of Mathematics
Volume225
Issue number1
DOIs
StatePublished - Apr 1 2018

Bibliographical note

Funding Information:
∗The research of the first-named author is supported in part by the NSF Grants DMS–1301567 and DMS–1600685. ∗∗ The research of the second-named author is supported in part by National Natu-ral Science Foundation of China (#11601087) and by Program of Shanghai Aca-demic/Technology Research Leader (#16XD1400400). Received December 13, 2016 and in revised form February 8, 2017

Publisher Copyright:
© 2018, Hebrew University of Jerusalem.

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