Poles of Eisenstein series and theta lifts for unitary groups

Chenyan Wu

Vol. 317 (2022), No. 1, 207–237

DOI: 10.2140/pjm.2022.317.207

Abstract

We derive a precise relation of poles of Eisenstein series associated to the cuspidal datum $\chi \otimes \sigma$ and the lowest occurrence of theta lifts of a cuspidal automorphic representation $\sigma$ of a unitary group, where $\chi$ 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