On a special value of the Ruelle L-function

Let X be a a complete hyperbolic threefold of a finite volume with only one cusp. For a unitary local system ρ of rank one on X, one may associte the Ruelle L-function Rρ(z). Suppose the restriction of ρ to the cusp is nontrivial. We will show that the Ruelle L-function has a pole at the origin whose order is equal to −2dimH(X, ρ). Moreover we will prove if dimH(X, ρ) is zero Rρ(0) is equal to the square of the FranzReidemeister torsion of (X, ρ). 1