Analytic torsion for arithmetic locally symmetric manifolds and approximation of \(L^2\)-torsion (Q2097933)

The motivation for this article came from applications of the Ray-Singer analytic torsion to study the growth of torsion in the cohomology of co-compact arithmetic groups, as shown in [\textit{N. Bergeron} and \textit{A. Venkatesh}, J. Inst. Math. Jussieu 12, No. 2, 391--447 (2013; Zbl 1266.22013)]. However, some arithmetic groups are not cocompact, then it is desirable to extend these results to non-cocompact lattices. The author's abstract summarized very well what is presented in the article and it is reproduced bellow. From the authors abstract: ``In this paper we define a regularized version of the analytic torsion for quotients of a symmetric space of non-positive curvature by arithmetic lattices. The definition is based on the study of the renormalized trace of the corresponding heat operators, which is defined as the geometric side of the Arthur trace formula applied to the heat kernel. Then we study the limiting behavior of the analytic torsion as the lattices run through a sequence of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for sequences of principal congruence subgroups, which converge to 1 at a fixed finite set of places and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the \(L^2\)-analytic torsion.''