  Let $M$ be a finite volume hyperbolic Riemann surface with arbitrary
signature, and let $\chi$ be an arbitrary $m$-dimensional multiplier system of
weight $k$. Let $R(s,\chi)$ be the associated Ruelle zeta function, and
$\varphi(s,\chi)$ the determinant of the scattering matrix. We prove the
functional equation that $R(s,\chi)\varphi(s,\chi) =
R(-s,\chi)\varphi(s,\chi)H(s,\chi)$ where $H(s,\chi)$ is a meromorphic function
of order one explicitly determined using the topological data of $M$ and of
$\chi$, and the trigonometric function $\sin(s)$. From this, we determine the
order of the divisor of $R(s,\chi)$ at $s=0$ and compute the lead coefficient
in its Laurent expansion at $s=0$. When combined with results by Kitano and by
Yamaguchi, we prove further instances of the Fried conjecture, which states
that the R-torsion of the above data is simply expressed in terms of
$R(0,\chi)$.
