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

Dihua Jiang; Chenyan Wu

doi:10.1007/s11856-018-1658-4

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

Dihua Jiang, Chenyan Wu

Mathematics

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2 Scopus citations

Abstract

In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations σ of symplectic groups Sp_2n(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 language	English (US)
Pages (from-to)	267-320
Number of pages	54
Journal	Israel Journal of Mathematics
Volume	225
Issue number	1
DOIs	https://doi.org/10.1007/s11856-018-1658-4
State	Published - 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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Periods and (χ, b)-factors of cuspidal automorphic forms of symplectic groups

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