{
  "id": "2105.06821",
  "version": "v2",
  "published": "2021-05-14T13:32:16.000Z",
  "updated": "2021-05-27T02:45:55.000Z",
  "title": "Atkinson's formula for the mean square of $ζ(s)$ with an explicit error term",
  "authors": [
    "Aleksander Simonič",
    "Valeriia V. Starichkova"
  ],
  "comment": "41 pages, 1 figure, 2 tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "We provide an explicit $O\\left(\\log^2{T}\\right)$-term of the celebrated Atkinson's formula for the error term $E(T)$ of the second power moment of the Riemann zeta-function on the critical line. As an application, we obtain an explicit version of well-known estimate $E(T)\\ll_{\\varepsilon} T^{\\frac{1}{3}+\\varepsilon}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-05-27T02:45:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11N37",
      "11Y35"
    ],
    "keywords": [
      "explicit error term",
      "mean square",
      "second power moment",
      "celebrated atkinsons formula",
      "explicit version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}