{
  "id": "2309.08057",
  "version": "v1",
  "published": "2023-09-14T22:48:14.000Z",
  "updated": "2023-09-14T22:48:14.000Z",
  "title": "Mean values of long Dirichlet polynomials with divisor coefficients",
  "authors": [
    "Fatma Cicek",
    "Alia Hamieh",
    "Nathan Ng"
  ],
  "comment": "38 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article, we prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lower order terms and a power saving error term. This is derived from a more general theorem on mean values of long smoothed Dirichlet polynomials that was previously established by the second and third authors. We thus establish a stronger form of a conjecture of Conrey and Gonek in the case of divisor functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-14T22:48:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26",
      "11M41",
      "11N37",
      "11N75"
    ],
    "keywords": [
      "long dirichlet polynomials",
      "mean value",
      "divisor coefficients",
      "long smoothed dirichlet polynomials",
      "power saving error term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}