  In this paper, we prove the entirety of loop group Eisenstein series induced
from cusp forms on the underlying finite dimensional group, by demonstrating
their absolute convergence on the full complex plane. This is quite in contrast
to the finite-dimensional setting, where such series only converge absolutely
in a right half plane (and have poles elsewhere coming from $L$-functions in
their constant terms). Our result is the $\Q$-analog of a theorem of A.
Braverman and D. Kazhdan from the function field setting, who previously showed
the analogous Eisenstein series are finite sums.
