{
  "id": "1205.2161",
  "version": "v1",
  "published": "2012-05-10T05:24:14.000Z",
  "updated": "2012-05-10T05:24:14.000Z",
  "title": "On the higher derivatives of Z(t) associated with the Riemann Zeta-Function",
  "authors": [
    "Kaneaki Matsuoka"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $Z(t)$ be the classical Hardy function in the theory of the Riemann zeta-function. The main result in this paper is that if the Riemann hypothesis is true then for any positive integer $n$ there exists a $t_{n}>0$ such that for $t>t_{n}$ the function $Z^{(n+1)}(t)$ has exactly one zero between consecutive zeros of $Z^{(n)}(t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-10T05:24:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "riemann zeta-function",
      "higher derivatives",
      "main result",
      "riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.2161M"
    }
  }
}