The torsion in symmetric powers on congruence subgroups of Bianchi groups.

In this paper we prove that for a fixed neat principal congruence subgroup of a Bianchi group the order of the torsion part of its second cohomology group with coefficients in an integral lattice associated with the mth symmetric power of the standard representation of SL2(C) grows exponentially in m2. We give upper and lower bounds for the growth rate. Our result extends a result of W. Müller and S. Marshall, who proved the corresponding statement for closed arithmetic 3-manifolds, to the finite-volume case. We also prove a limit multiplicity formula for combinatorial Reidemeister torsions on higher-dimensional hyperbolic manifolds. [ABSTRACT FROM AUTHOR]