  Bismut and Zhang computed the ratio of the Ray-Singer and the combinatorial
torsions corresponding to non-unitary representations of the fundamental group.
In this note we show that for representations which belong to a connected
component containing a unitary representation the Bismut-Zhang formula follows
rather easily from the Cheeger-Mueller theorem, i.e. from the equality of the
two torsions on the set of unitary representations. The proof uses the fact
that the refined analytic torsion is a holomorphic function on the space of
representations.

Spectral Theory;Differential Geometry