Poles of Eisenstein series and theta lifts for unitary groups

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.