{
  "id": "2005.13726",
  "version": "v1",
  "published": "2020-05-28T01:14:25.000Z",
  "updated": "2020-05-28T01:14:25.000Z",
  "title": "Arithmetic Groups and the Lehmer Conjecture",
  "authors": [
    "Lam Pham",
    "François Thilmany"
  ],
  "comment": "16 pages",
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "In this paper, we generalize a result of Sury and show that uniform discreteness of cocompact lattices in higher rank semisimple Lie groups is equivalent to a weak form of Lehmer's conjecture. We also survey some related conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-28T01:14:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "20G30",
      "11E57"
    ],
    "keywords": [
      "lehmer conjecture",
      "arithmetic groups",
      "higher rank semisimple lie groups",
      "cocompact lattices",
      "uniform discreteness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}