{
  "id": "2406.06066",
  "version": "v1",
  "published": "2024-06-10T07:22:18.000Z",
  "updated": "2024-06-10T07:22:18.000Z",
  "title": "Note on the asymptotic of the auxiliary function",
  "authors": [
    "Juan Arias de Reyna"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "To define an explicit regions without zeros of $\\mathop{\\mathcal R}(s)$, in a previous paper we obtained an approximation to $\\mathop{\\mathcal R}(s)$ of type $f(s)(1+U)$ with $|U|< 1$. But this $U$ do not tend to zero when $t\\to+\\infty$. In the present paper we get an approximation of the form $f(s)(1+o(t))$. We precise here Siegel's result, following his reasoning. This is essential to get the last Theorems in Siegel's paper about $\\mathop{\\mathcal R}(s)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-10T07:22:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "30D99"
    ],
    "keywords": [
      "auxiliary function",
      "asymptotic",
      "explicit regions",
      "siegels paper",
      "approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}