Analytic torsion of arithmetic quotients of the symmetric space $${\rm SL} (n,\mathbb{R})/ {\rm SO}(n)$$ SL ( n , R ) / SO ( n )

Abstract

In this paper we define a regularized version of the analytic torsion for arithmetic quotients of the symmetric space $${{\rm SL}(n,\mathbb{R})/ {\rm SO}(n)}$$ . 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 operator.