{
  "id": "1001.1055",
  "version": "v1",
  "published": "2010-01-07T14:53:41.000Z",
  "updated": "2010-01-07T14:53:41.000Z",
  "title": "Simultaneous zeros of a Cubic and Quadratic form",
  "authors": [
    "Jahan Zahid"
  ],
  "comment": "19 pages",
  "doi": "10.1112/jlms/jdr018",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We verify a conjecture of Emil Artin, for the case of a Cubic and Quadratic form over any $p$-adic field, provided the cardinality of the residue class field exceeds 293. That is any Cubic and Quadratic form with at least 14 variables has a non-trivial $p$-adic zero, with the aforementioned condition on the residue class field. A crucial step in the proof, involves generalizing a $p$-adic minimization procedure due to W. M. Schmidt to hold for systems of forms of arbitrary degrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-07T14:53:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D88",
      "11D72",
      "11G25",
      "14G20"
    ],
    "keywords": [
      "quadratic form",
      "simultaneous zeros",
      "residue class field exceeds",
      "adic minimization procedure",
      "emil artin"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}