On the asymptotics of the analytic torsion for compact hyperbolic orbifolds

We study the analytic torsion of odd-dimensional hyperbolic orbifolds $Gamma backslash mathbb{H}^{2n+1}$, depending on a representation of $Gamma$. Our main goal is to understand the asymptotic behavior of the analytic torsion with respect to sequences of representations associated to rays of highest weights.