Approximation of L²-analytic torsion for arithmetic quotients of the symmetric space SL(n,ℝ)/SO(n)

2017/09/22 by Jasmin Matz, Matz, Jasmin, Werner Mueller +1
Mathematics · #58J52 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1709.07764

openalex publication_date 2017/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [MzM] we defined a regularized analytic torsion for quotients of the symmetric space SL(n,ℝ)/SO(n) by arithmetic lattices. In this paper we study the limiting behaviour of the analytic torsion as the lattices run through sequences of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for principal congruence subgroups and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the L²-analytic torsion.

Citations

• On Certain L-Functions
• On the growth of torsion in the cohomology of arithmetic groups

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