{
  "id": "1709.07764",
  "version": "v1",
  "published": "2017-09-22T14:06:32.000Z",
  "updated": "2017-09-22T14:06:32.000Z",
  "title": "Approximation of $L^2$-analytic torsion for arithmetic quotients of the symmetric space $\\mathrm{SL}(n,\\mathbb{R})/\\mathrm{SO}(n)$",
  "authors": [
    "Jasmin Matz",
    "Werner Mueller"
  ],
  "comment": "47 pages. arXiv admin note: text overlap with arXiv:1607.04676",
  "categories": [
    "math.RT"
  ],
  "abstract": "In [MzM] we defined a regularized analytic torsion for quotients of the symmetric space $\\mathrm{SL}(n,\\mathbb{R})/\\mathrm{SO}(n)$ 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 $L^2$-analytic torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-22T14:06:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J52"
    ],
    "keywords": [
      "symmetric space",
      "arithmetic quotients",
      "approximation",
      "main result states",
      "principal congruence subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}