The analytic torsion and its asymptotic behaviour for sequences of hyperbolic manifolds of finite volume

Abstract

In this paper we study the regularized analytic torsion of finite volume hyperbolic manifolds. We consider sequences of coverings Xi of a fixed hyperbolic orbifold X0. Our main result is that for certain sequences of coverings and strongly acyclic flat bundles the analytic torsion divided by the index of the covering converges to the L2-torsion. Our results apply to certain sequences of arithmetic groups, in particular to sequences of principal congruence subgroups of SO0(d,1)(Z) and to sequences of principal congruence subgroups or Hecke subgroups of Bianchi groups.