Poles of Eisenstein series and theta lifts for unitary groups

TL;DR

This paper establishes a detailed connection between the poles of Eisenstein series and the lowest occurrence of theta lifts in the context of unitary groups, advancing understanding of automorphic forms and their lifts.

Contribution

It provides a precise relation linking Eisenstein series poles to theta lift occurrences for unitary groups, with novel computations of period integrals of truncated Eisenstein series.

Findings

Explicit relation between Eisenstein series poles and theta lift lowest occurrence

Computed period integrals of truncated Eisenstein series

Enhanced understanding of automorphic representations 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.