Vol. 317, No. 1, 2022

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Poles of Eisenstein series and theta lifts for unitary groups

Chenyan Wu

Vol. 317 (2022), No. 1, 207–237
Abstract

We derive a precise relation of poles of Eisenstein series associated to the cuspidal datum χ σ and the lowest occurrence of theta lifts of a cuspidal automorphic representation σ of a unitary group, where χ is a conjugate self-dual character. A key ingredient of the proof is the computation of period integrals of truncated Eisenstein series.

Keywords
theta correspondence, Eisenstein series, $L$-function, period integral, Arthur truncation
Mathematical Subject Classification
Primary: 11F27, 11F30, 11F67, 11M36
Milestones
Received: 1 June 2021
Revised: 9 January 2022
Accepted: 12 February 2022
Published: 19 June 2022
Authors
Chenyan Wu
School of Mathematics and Statistics
The University of Melbourne
Victoria
Australia