{
  "id": "1811.05277",
  "version": "v1",
  "published": "2018-11-13T13:22:01.000Z",
  "updated": "2018-11-13T13:22:01.000Z",
  "title": "Zeros of a polynomial of $ζ^{(j)}(s)$",
  "authors": [
    "Tomokazu Onozuka"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give results on zeros of a polynomial of $\\zeta(s),\\zeta'(s),\\ldots,\\zeta^{(k)}(s)$. First, we give a zero free region and prove that there exist zeros corresponding to the trivial zeros of the Riemann zeta function. Next, we estimate the number of zeros whose imaginary part is in $(1,T)$. Finally, we study the distribution of the real part and the imaginary part of zeros, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-13T13:22:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "polynomial",
      "imaginary part",
      "riemann zeta function",
      "zero free region",
      "real part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}