{
  "id": "1010.1926",
  "version": "v2",
  "published": "2010-10-10T14:58:43.000Z",
  "updated": "2011-04-13T12:48:08.000Z",
  "title": "A proof of the S-genus identities for ternary quadratic forms",
  "authors": [
    "Alexander Berkovich",
    "Jonathan Hanke",
    "William Jagy"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we prove the main conjectures of Berkovich and Jagy about weighted averages of representation numbers over an S-genus of ternary lattices (defined below) for any odd squarefree S \\in N. We do this by reformulating them in terms of local quantities using the Siegel-Weil and Conway-Sloane formulas, and then proving the necessary local identities. We conclude by conjecturing generalized formulas valid over certain totally real number fields as a direction for future work.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-13T12:48:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11E20",
      "11E25",
      "11F27",
      "11F30",
      "11F37"
    ],
    "keywords": [
      "ternary quadratic forms",
      "s-genus identities",
      "totally real number fields",
      "necessary local identities",
      "local quantities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.1926B"
    }
  }
}