In this paper we consider the cohomology of a closed arithmetic hyperbolic -manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of . The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomology grows exponentially as the local system grows. We also consider the twisted Ruelle zeta function of a closed arithmetic hyperbolic -manifold, and we express the leading coefficient of its Laurent expansion at the origin in terms of the orders of the torsion subgroups of the cohomology.
"On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds." Duke Math. J. 162 (5) 863 - 888, 1 April 2013. https://doi.org/10.1215/00127094-2080850