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Abstract
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We derive a precise relation of poles of Eisenstein series associated to the cuspidal datum
and
the lowest occurrence of theta lifts of a cuspidal automorphic representation
of a unitary
group, where
is a conjugate self-dual character. A key ingredient of the proof is the computation of
period integrals of truncated Eisenstein series.
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Keywords
theta correspondence, Eisenstein series, $L$-function,
period integral, Arthur truncation
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Mathematical Subject Classification
Primary: 11F27, 11F30, 11F67, 11M36
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Milestones
Received: 1 June 2021
Revised: 9 January 2022
Accepted: 12 February 2022
Published: 19 June 2022
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