  We discuss semiclassical expansions around a class of classical string
configurations lying in AdS_3 x S^1 using the Pohlmeyer-reduced from of the
AdS_5 x S^5 superstring theory. The Pohlmeyer reduction of the AdS_5 x S^5
superstring theory is a gauged Wess-Zumino-Witten model with an integrable
potential and two-dimensional fermionic fields. It was recently conjectured
that the quantum string partition function is equal to the quantum reduced
theory partition function. Continuing the previous paper (arXiv:0906.3800)
where arbitrary solutions in AdS_2 x S^2 and homogeneous solutions were
considered, we provide explicit demonstration of this conjecture at the
one-loop level for several string solutions in AdS_3 x S^1 embedded into AdS_5
x S^5. Quadratic fluctuations derived in the reduced theory for inhomogeneous
strings are equivalent to respective fluctuations found from the Nambu action
in the original string theory. We also show the equivalence of fluctuation
frequencies for homogeneous strings with both the orbital momentum and the
winding on a big circle of S^5.
