{
  "id": "2401.10936",
  "version": "v1",
  "published": "2024-01-17T09:29:28.000Z",
  "updated": "2024-01-17T09:29:28.000Z",
  "title": "On the lowest zero of Dedekind zeta function",
  "authors": [
    "Sushant Kala"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\zeta_K(s)$ denote the Dedekind zeta-function associated to a number field $K$. In this paper, we give an effective upper bound for the height of first non-trivial zero other than $1/2$ of $\\zeta_K(s)$ under the generalized Riemann hypothesis. This is a refinement of the earlier bound obtained by Omar Sami.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-17T09:29:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R42",
      "11M26"
    ],
    "keywords": [
      "dedekind zeta function",
      "lowest zero",
      "first non-trivial zero",
      "dedekind zeta-function",
      "earlier bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}