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arXiv · 2002.08551

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

Chenyan Wu
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Abstract

We give constraints on the existence of $(\chi,b)$-factors in the global $A$-parameter of a genuine cuspidal automorphic representation $\sigma$ of a metaplectic group in terms of the invariant, lowest occurrence index, of theta lifts to odd orthogonal groups. We also give a refined result that relates the invariant, first occurrence index, to non-vanishing of period integrals of residues of Eisenstein series associated to the cuspidal datum $\chi\otimes\sigma$. This complements our previous results for symplectic groups.

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BibTeXRIS

Chenyan Wu. 2020-02-20. Periods and $(\chi,b)$-factors of Cuspidal Automorphic Forms of Metaplectic Groups. https://doi.org/10.1016/j.jnt.2022.03.010

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