{
  "id": "1210.3097",
  "version": "v1",
  "published": "2012-10-11T00:43:11.000Z",
  "updated": "2012-10-11T00:43:11.000Z",
  "title": "The explicit upper bound of the multiple integral of $S(t)$ on the Riemann Hypothesis",
  "authors": [
    "Takahiro Wakasa"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove explicit upper bounds of the function $S_m(T)$, defined by the repeated integration of the argument of the Riemann zeta-function. The explicit upper bound of $S(T)$ and $S_1(T)$ have already been obtained by A. Fujii. Our result is a generalization of Fujii's results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-11T00:43:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit upper bound",
      "multiple integral",
      "riemann hypothesis",
      "riemann zeta-function",
      "fujiis results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.3097W"
    }
  }
}