{
  "id": "1612.01394",
  "version": "v1",
  "published": "2016-12-05T15:30:16.000Z",
  "updated": "2016-12-05T15:30:16.000Z",
  "title": "Two elementary formulae and some complicated properties for Mertens function",
  "authors": [
    "Rong Qiang Wei"
  ],
  "comment": "12 pages, 8 figures, 1 table",
  "categories": [
    "math.NT"
  ],
  "abstract": "Two elementary formulae for Mertens function $M(n)$ are obtained. With these formulae, $M(n)$ can be calculated directly and simply, which can be easily implemented by computer. $M (1) \\sim M (2 \\times 10^7) $ are calculated one by one. Based on these $2\\times 10^7$ samples, some of the complicated properties for Mertens function $M(n)$, its 18144 zeros, the 11040 local maximum/minimum between two neighbor zeros, and the relation with the cumulative sum of the squarefree integers, are understood numerically and empirically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-05T15:30:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mertens function",
      "elementary formulae",
      "complicated properties",
      "local maximum/minimum",
      "neighbor zeros"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}