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

We give constraints on the existence of (χ,b)-factors in the global A-parameter of a genuine cuspidal automorphic representation σ 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 invari...

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Bibliographic Details
Published inJournal of number theory Vol. 241; pp. 262 - 296
Main Author Wu, Chenyan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2022
Subjects
Arthur parameters
Arthur truncation of Eisenstein series and residues
Periods of automorphic forms
Poles of L-functions
Theta correspondence
Poles of L-functions
Arthur truncation of Eisenstein series and residues
Theta correspondence
Periods of automorphic forms
Arthur parameters
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Summary:We give constraints on the existence of (χ,b)-factors in the global A-parameter of a genuine cuspidal automorphic representation σ 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 χ⊗σ. This complements our previous results for symplectic groups.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2022.03.010