{
  "id": "1712.01519",
  "version": "v1",
  "published": "2017-12-05T08:13:45.000Z",
  "updated": "2017-12-05T08:13:45.000Z",
  "title": "A New Equation Involving Merten's Function And It's Implications",
  "authors": [
    "Irfan Okay"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "One of the many equivalent statements for Riemann Hypothesis is that Merten's function $M(x)$, which is related to square free integers, is of order $O(x^{1/2+\\epsilon})$. In this paper, we derive an exact equation involving Merten's function, which leads to a promising new technique for obtaining a nontrivial bound for $M(x)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-05T08:13:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mertens function",
      "implications",
      "square free integers",
      "equivalent statements",
      "exact equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}