  We analyze the effects of zeta-function regularization on the evaluation of
quantum corrections to spinning strings. Previously, this method was applied in
the sl(2) subsector and yielded agreement to third order in perturbation theory
with the quantum string Bethe ansatz. In this note we discuss related sums and
compare zeta-function regularization against exact evaluation of the sums,
thereby showing that the zeta-function regularized expression misses out
perturbative as well as non-perturbative terms. In particular, this may imply
corrections to the proposed quantum string Bethe equations. This also explains
the previously observed discrepancy between the semi-classical string and the
quantum string Bethe ansatz in the regime of large winding number.
