{
  "id": "math/0511092",
  "version": "v1",
  "published": "2005-11-03T17:04:05.000Z",
  "updated": "2005-11-03T17:04:05.000Z",
  "title": "A note on S(T) and the zeros of the Riemann zeta-function",
  "authors": [
    "D. A. Goldston",
    "S. M. Gonek"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi S(t)$ denote the argument of the Riemann zeta-function at the point $\\frac12+it$. Assuming the Riemann Hypothesis, we sharpen the constant in the best currently known bounds for $S(t)$ and for the change of $S(t)$ in intervals. We then deduce estimates for the largest multiplicity of a zero of the zeta-function and for the largest gap between the zeros.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-03T17:04:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26"
    ],
    "keywords": [
      "riemann zeta-function",
      "riemann hypothesis",
      "deduce estimates",
      "largest multiplicity",
      "largest gap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11092G"
    }
  }
}