{
  "id": "2406.07014",
  "version": "v1",
  "published": "2024-06-11T07:15:19.000Z",
  "updated": "2024-06-11T07:15:19.000Z",
  "title": "Riemann's Auxiliary Function. Right limit of zeros",
  "authors": [
    "Juan Arias de Reyna"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Numerical data suggest that the zeros $\\rho$ of the auxiliary Riemann function in the upper half-plane satisfy $\\mathop{\\mathrm{Re}}(\\rho)<1$. We show that this is true for those zeros with $\\mathop{\\mathrm{Im}}(\\rho)> 3.9211\\dots10^{65}$. We conjecture that this is true for all of them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-11T07:15:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "30D99"
    ],
    "keywords": [
      "riemanns auxiliary function",
      "right limit",
      "auxiliary riemann function",
      "upper half-plane satisfy",
      "numerical data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}