{
  "id": "1407.1222",
  "version": "v2",
  "published": "2014-07-04T13:23:16.000Z",
  "updated": "2014-12-08T20:57:30.000Z",
  "title": "Average number of squares dividing mn",
  "authors": [
    "Andrew V. Lelechenko"
  ],
  "comment": "12 pages, 1 figure",
  "journal": "Visn. Odessk. Univ., Ser. Mat. Mekh., 2014, vol. 19, #2 (22), p. 52-65",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the asymptotic behaviour of $\\sum_{m,n\\le x} \\tau_{1,2}(mn)$, where $\\tau_{1,2}(n) = \\sum_{a b^2 = n} 1$, using multidimensional Perron formula and complex integration method. An asymptotic formula with an error term $O(x^{10/7})$ is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-04T13:23:16.000Z",
      "title": "Average number of squares, dividing mn",
      "abstract": "We study the asymptotic behaviour of $\\sum_{m,n\\le x} \\tau_{1,2}(mn)$, where $\\tau_{1,2}(n) = \\sum_{a b^2 = n} 1$, using multidimensional Perron formula and complex integration method. An asymptotic formula with an error term $O( x^{1.47537})$ is proven.",
      "comment": "11 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-08T20:57:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11N37"
    ],
    "keywords": [
      "average number",
      "dividing mn",
      "multidimensional perron formula",
      "complex integration method",
      "asymptotic behaviour"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1222L"
    }
  }
}