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.
Keywords
theta correspondence, Eisenstein series, $L$-function,
period integral, Arthur truncation