APPROXIMATION OF L-2-ANALYTIC TORSION FOR ARITHMETIC QUOTIENTS OF THE SYMMETRIC SPACE SL(n, R) / SO(n)

In [31] we defined a regularized analytic torsion for quotients of the symmetric space SL.n; R /= SO.n/ by arithmetic lattices. In this paper we study the limiting behavior of the analytic torsion as the lattices run through sequences of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for principal congruence subgroups and strongly acyclic at bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the L2 -analytic torsion.