{
  "id": "1609.08481",
  "version": "v1",
  "published": "2016-09-27T14:44:10.000Z",
  "updated": "2016-09-27T14:44:10.000Z",
  "title": "Stable lattices and the diagonal group",
  "authors": [
    "Uri Shapira",
    "Barak Weiss"
  ],
  "comment": "This paper was part of the paper \"On stable lattices and the diagonal group\" (arXiv:1309.4025) which was split into three shorter papers (now all on arXiv) following the referee's request",
  "journal": "Journal of the European Mathematical Society. Volume 18, Issue 8, 2016, pp. 1753 - 1767",
  "categories": [
    "math.DS"
  ],
  "abstract": "Inspired by work of McMullen, we show that any orbit of the diagonal group in the space of lattices accumulates on the set of stable lattices. As consequences, we settle a conjecture of Ramharter concerning the asymptotic behaviour of the Mordell constant, and reduce Minkowski's conjecture on products of linear forms to a geometric question, yielding two new proofs of the conjecture in dimensions up to 7.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-27T14:44:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diagonal group",
      "stable lattices",
      "reduce minkowskis conjecture",
      "asymptotic behaviour",
      "lattices accumulates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}