The Asymptotics of the Ray-Singer Analytic Torsion of Hyperbolic 3-manifolds

In this paper we consider the analytic torsion of a closed hyperbolic 3-manifold associated with the mth symmetric power of the standard representation of SL(2C) and we study its asymptotic behavior as mtends to infinity. The leading coefficient of the asymptotic formula is given by the volume of the hyperbolic 3-manifold. It follows that the Reidemeister torsion associated with the symmetric powers determines the volume of a closed hyperbolic 3-manifold.