{
  "id": "2407.06681",
  "version": "v1",
  "published": "2024-07-09T08:57:20.000Z",
  "updated": "2024-07-09T08:57:20.000Z",
  "title": "Simple bounds for the auxiliary function of Riemann",
  "authors": [
    "Juan Arias de Reyna"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give simple numerical bounds for $\\zeta(s)$, $\\vartheta(s)$, $\\mathop{\\mathcal R}(s)$, $Z(t)$, for use in the numerical computation of these functions. The purpose of the paper is to give bounds for several functions needed in the calculation of $\\zeta(s)$ and $Z(t)$. We are not pretending to have any originality. Our object is to be useful as a reference in our work for simple (simple to compute and simple to check) bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-09T08:57:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "30D99"
    ],
    "keywords": [
      "auxiliary function",
      "simple bounds",
      "simple numerical bounds",
      "calculation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}