{
  "id": "1101.2951",
  "version": "v2",
  "published": "2011-01-15T08:32:26.000Z",
  "updated": "2011-01-30T22:45:28.000Z",
  "title": "On representation of an integer as the sum of three squares and the ternary quadratic forms with the discriminants p^2, 16p^2",
  "authors": [
    "Alexander Berkovich",
    "Will Jagy"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let s(n) be the number of representations of n as the sum of three squares. We prove a remarkable new identity for s(p^2n)- ps(n) with p being an odd prime. This identity makes nontrivial use of ternary quadratic forms with discriminants p^2 and 16p^2. These forms are related by Watson's transformations. To prove this identity we employ the Siegel--Weil and the Smith--Minkowski product formulas.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-30T22:45:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ternary quadratic forms",
      "representation",
      "discriminants",
      "smith-minkowski product formulas",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}