{
  "id": "1312.4650",
  "version": "v2",
  "published": "2013-12-17T05:32:47.000Z",
  "updated": "2015-04-20T09:09:10.000Z",
  "title": "On the Local-Global Principle for Integral Apollonian-3 Circle Packings",
  "authors": [
    "Xin Zhang"
  ],
  "comment": "40 pages",
  "categories": [
    "math.NT",
    "math.GR",
    "math.SP"
  ],
  "abstract": "In this paper we study the integral properties of Apollonian-3 circle packings, which are variants of the standard Apollonian circle packings. Specifically, we study the reduction theory, formulate a local-global conjecture, and prove a density one version of this conjecture. Along the way, we prove a uniform spectral gap for congruence towers of the symmetry group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-17T05:32:47.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-20T09:09:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local-global principle",
      "standard apollonian circle packings",
      "uniform spectral gap",
      "reduction theory",
      "symmetry group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4650Z"
    }
  }
}