{
  "id": "math/0311162",
  "version": "v1",
  "published": "2003-11-11T08:25:54.000Z",
  "updated": "2003-11-11T08:25:54.000Z",
  "title": "On some reasons for doubting the Riemann hypothesis",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|\\zeta(1/2+it)|$ on the critical line, and zeros of a class of convolution functions. The first two topics are classical, and the remaining ones are connected with the author's research.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-11T08:25:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "riemann hypothesis",
      "lehmer phenomenon",
      "davenport-heilbronn zeta-function",
      "mean values",
      "convolution functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11162I"
    }
  }
}