{
  "id": "1401.2310",
  "version": "v1",
  "published": "2014-01-10T12:35:40.000Z",
  "updated": "2014-01-10T12:35:40.000Z",
  "title": "The sum of divisors of a quadratic form",
  "authors": [
    "Lilu Zhao"
  ],
  "comment": "Accepted by Acta Arithmetica",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the sum of divisors of the quadratic form $m_1^2+m_2^2+m_3^2$. Let $$S_3(X)=\\sum_{1\\le m_1,m_2,m_3\\le X}\\tau(m_1^2+m_2^2+m_3^2).$$ We obtain the asymptotic formula $$S_3(X)=C_1X^3\\log X+ C_2X^3+O(X^2\\log^7 X),$$ where $C_1,C_2$ are two constants. This improves upon the error term $O_\\varepsilon(X^{8/3+\\varepsilon})$ obtained by Guo and Zhai.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-10T12:35:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic form",
      "error term",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2310Z"
    }
  }
}