{
  "id": "1606.03733",
  "version": "v1",
  "published": "2016-06-12T15:47:30.000Z",
  "updated": "2016-06-12T15:47:30.000Z",
  "title": "On the $a$-points of the derivatives of the Riemann zeta function",
  "authors": [
    "Tomokazu Onozuka"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove three results on the $a$-points of the derivatives of the Riemann zeta function. The first result is a formula of the Riemann-von Mangoldt type; we estimate the number of the $a$-points of the derivatives of the Riemann zeta function. The second result is on certain exponential sum involving $a$-points. The third result is an analogue of the zero density theorem. We count the $a$-points of the derivatives of the Riemann zeta function in $1/2-(\\log\\log T)^2/\\log T<\\Re s<1/2+(\\log\\log T)^2/\\log T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-12T15:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "riemann zeta function",
      "derivatives",
      "riemann-von mangoldt type",
      "zero density theorem",
      "first result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}