{
  "id": "1011.3997",
  "version": "v1",
  "published": "2010-11-17T16:39:00.000Z",
  "updated": "2010-11-17T16:39:00.000Z",
  "title": "On the Gram's Law in the Theory of Riemann Zeta Function",
  "authors": [
    "M. A. Korolev"
  ],
  "comment": "35 pages, 1 figure",
  "journal": "Izvestiya: Mathematics(2012), 76(2):275",
  "doi": "10.4213/im5558",
  "categories": [
    "math.NT"
  ],
  "abstract": "Some statements concerning the distribution of imaginary parts of zeros of the Riemann zeta\\,-function are established. These assertions are connected with so\\,-called `Gram's law' or `Gram's rule'. In particular, we give a proof of several Selberg's formulae stated him without proof in his paper `The Zeta Function and the Riemann Hypothesis' (1946), and some of their equivalents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-17T16:39:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26"
    ],
    "keywords": [
      "riemann zeta function",
      "grams law",
      "imaginary parts",
      "grams rule",
      "riemann hypothesis"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Izvestiya: Mathematics",
      "year": 2012,
      "month": "Apr",
      "volume": 76,
      "number": 2,
      "pages": 275
    },
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012IzMat..76..275K"
    }
  }
}