Torsion à coefficients dans les puissances symétriques pour les groupes de Bianchi

International audienceIn 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 to the m-th symmetric power of the standard representation of SL 2 (C) grows exponentially in m 2. We give upper and lower bounds for the growth rate. Our result extends a 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