{
  "id": "2002.09466",
  "version": "v1",
  "published": "2020-02-21T18:34:49.000Z",
  "updated": "2020-02-21T18:34:49.000Z",
  "title": "Averages of long Dirichlet polynomials",
  "authors": [
    "Sandro Bettin",
    "J. Brian Conrey"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the asymptotic behavior of the mean square of truncations of the Dirichlet series of $\\zeta(s)^k$. We discuss the connections of this problem with that of the variance of the divisor function in short intervals and in arithmetic progressions, reviewing the recent results on this topic. Finally, we show how these results can all be proved assuming a suitable version of the moments conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-21T18:34:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11M06",
      "11M50"
    ],
    "keywords": [
      "long dirichlet polynomials",
      "moments conjecture",
      "dirichlet series",
      "asymptotic behavior",
      "divisor function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}