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 $X_i$ of a fixed hyperbolic orbifold $X_0$. 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 $L^2$-torsion. Our results apply to certain sequences of arithmetic groups, in particular to sequences of principal congruence subgroups of $\SO^0(d,1)(\Z)$ and to sequences of principal congruence subgroups or Hecke subgroups of Bianchi groups.