{
  "id": "1310.6158",
  "version": "v3",
  "published": "2013-10-23T08:59:23.000Z",
  "updated": "2015-04-01T14:27:17.000Z",
  "title": "Cubic polynomials represented by norm forms",
  "authors": [
    "A. J. Irving"
  ],
  "comment": "40 pages, V2 contains some Minor corrections, V3 includes the bibliography which was missing in V2",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that for an irreducible cubic $f\\in\\mathbb Z[x]$ and a full norm form $\\mathbf N(x_1,\\ldots,x_k)$ for a number field $K/\\mathbb Q$ satisfying certain hypotheses the variety $f(t)=\\mathbf N(x_1,\\ldots,x_k)\\ne 0$ satisfies the Hasse principle. Our proof uses sieve methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-30T09:05:57.000Z",
      "comment": "40 pages, V2 contains some Minor corrections",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-01T14:27:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11D57",
      "11N36"
    ],
    "keywords": [
      "cubic polynomials",
      "full norm form",
      "number field",
      "hasse principle",
      "sieve methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6158I"
    }
  }
}