{
  "id": "1411.6945",
  "version": "v1",
  "published": "2014-11-25T18:05:29.000Z",
  "updated": "2014-11-25T18:05:29.000Z",
  "title": "Local Descriptions of Roots of Cubic Equations over P-adic Fields",
  "authors": [
    "Mansoor Saburov",
    "Mohd Ali Khameini Ahmad"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT",
    "math.AC",
    "math.RA"
  ],
  "abstract": "The most frequently asked question in the $p-$adic lattice models of statistical mechanics is that whether a root of a polynomial equation belongs to domains $\\mathbb{Z}_p^{*}, \\ \\mathbb{Z}_p\\setminus\\mathbb{Z}_p^{*}, \\ \\mathbb{Z}_p, \\ \\mathbb{Q}_p\\setminus\\mathbb{Z}_p^{*}, \\ \\mathbb{Q}_p\\setminus\\left(\\mathbb{Z}_p\\setminus\\mathbb{Z}_p^{*}\\right), \\ \\mathbb{Q}_p\\setminus\\mathbb{Z}_p, \\ \\mathbb{Q}_p $ or not. However, this question was open even for lower degree polynomial equations. In this paper, we give local descriptions of roots of cubic equations over the $p-$adic fields for $p>3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-25T18:05:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic equations",
      "local descriptions",
      "p-adic fields",
      "lower degree polynomial equations",
      "polynomial equation belongs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6945S"
    }
  }
}