{
  "id": "1106.4806",
  "version": "v2",
  "published": "2011-06-23T19:51:15.000Z",
  "updated": "2011-06-27T19:51:48.000Z",
  "title": "The 4.36-th moment of the Riemann zeta-function",
  "authors": [
    "Maksym Radziwill"
  ],
  "comment": "10 pages; Fixed errors in Section 3. Proof of Thm 2 (now Corollary 1) shorter; Added a few comments following Proposition 1",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "Conditionally on the Riemann Hypothesis we obtain bounds of the correct order of magnitude for the 2k-th moment of the Riemann zeta-function for all positive real k < 2.181. This provides for the first time an upper bound of the correct order of magnitude for some k > 2; the case of k = 2 corresponds to a classical result of Ingham. We prove our result by establishing a connection between moments with k > 2 and the so-called \"twisted fourth moment\". This allows us to appeal to a recent result of Hughes and Young. Furthermore we obtain a point-wise bound for |zeta(1/2 + it)|^{2r} (with 0 < r < 1) that can be regarded as a multiplicative analogue of Selberg's bound for S(T). We also establish asymptotic formulae for moments (k < 2.181) slightly off the half-line.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-27T19:51:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M50"
    ],
    "keywords": [
      "riemann zeta-function",
      "correct order",
      "2k-th moment",
      "riemann hypothesis",
      "twisted fourth moment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4806R"
    }
  }
}