{
  "id": "1108.0135",
  "version": "v1",
  "published": "2011-07-31T05:01:49.000Z",
  "updated": "2011-07-31T05:01:49.000Z",
  "title": "Computing the Mertens function on a GPU",
  "authors": [
    "Eugene Kuznetsov"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A GPU implementation of an algorithm to compute the Mertens function in O(x2/3+{\\ko}) time is discussed. Results for x up to $10^{22}$, and a new extreme value for $M(x)/x^{1/2}$, -0.585768 ($M(x) \\approx -1.996 \\ast 10^9$ at $x \\approx 1.161 \\ast 10^{19}$), are reported.An approximate algorithm is used to examine values of M(x) for x up to $\\exp{(10^{15})}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-31T05:01:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mertens function",
      "gpu implementation",
      "extreme value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.0135K"
    }
  }
}