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arXiv · 1507.03297

Periods and $(\chi,b)$-factors of Cuspidal Automorphic Forms of Symplectic Groups

Dihua Jiang·Chenyan Wu
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Abstract

In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations $\sigma$ of symplectic groups $\mathrm{Sp}_{2n}(\mathbb{A})$, which detects the right-most pole of the $L$-function $L(s,\sigma\times\chi)$ for some character $\chi$ of $F^\times\backslash\mathbb{A}^\times$ of order at most $2$, and hence the occurrence of a simple global Arthur parameter $(\chi,b)$ in the global Arthur parameter $\psi$ attached to $\sigma$. We also give a characterisation of first occurrences of theta correspondence by (regularised) period integrals of residues of certain Eisenstein series.

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Dihua Jiang, Chenyan Wu. 2015-07-13. Periods and $(\chi,b)$-factors of Cuspidal Automorphic Forms of Symplectic Groups. https://doi.org/10.1007/s11856-018-1658-4

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