{
  "id": "2107.03191",
  "version": "v1",
  "published": "2021-07-07T13:01:09.000Z",
  "updated": "2021-07-07T13:01:09.000Z",
  "title": "An extension to the complex plane of the Riemann-Siegel Z function",
  "authors": [
    "Giovanni Lodone"
  ],
  "comment": "40 pages,3 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "The usual Riemann-Siegel Z(t) is a real-valued function. We construct a complex function depending from t and from distance from critical line. It is linked to Riemann Xi(s) function by the same real scaling factor of the usual Riemann-Siegel Z(t) on critical line. Errors are not greater than the errors of Riemann-Siegel Z(t) on the critical line, while this result covers at least the whole critical strip.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-07T13:01:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "complex plane",
      "critical line",
      "usual riemann-siegel",
      "real scaling factor",
      "riemann xi"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}