{
  "id": "0908.2008",
  "version": "v1",
  "published": "2009-08-14T03:50:39.000Z",
  "updated": "2009-08-14T03:50:39.000Z",
  "title": "Bounding |ζ(1/2 + it)| on the Riemann hypothesis",
  "authors": [
    "Vorrapan Chandee",
    "Kannan Soundararajan"
  ],
  "comment": "8 pages",
  "doi": "10.1112/blms/bdq095",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "In 1924 Littlewood showed that, assuming the Riemann Hypothesis, for large t there is a constant C such that |\\zeta(1/2+it)| \\ll \\exp(C\\log t/\\log \\log t). In this note we show how the problem of bounding |\\zeta(1/2+it)| may be framed in terms of minorizing the function \\log ((4+x^2)/x^2) by functions whose Fourier transforms are supported in a given interval, and drawing upon recent work of Carneiro and Vaaler we find the optimal such minorant. Thus we establish that any C> (\\log 2)/2 is permissible in Littlewood's result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-14T03:50:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "riemann hypothesis",
      "fourier transforms",
      "littlewoods result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2008C"
    }
  }
}