{
  "id": "math/9804051",
  "version": "v1",
  "published": "1998-04-08T20:51:38.000Z",
  "updated": "1998-04-08T20:51:38.000Z",
  "title": "Solubility of Systems of Quadratic Forms",
  "authors": [
    "Greg Martin"
  ],
  "comment": "4 pages",
  "journal": "Bull. London Math. Soc. 29 (1997), 385-388",
  "categories": [
    "math.NT"
  ],
  "abstract": "We derive an upper bound for the least number of variables needed to guarantee that a system of t quadratic forms (t>=2) over a field F has a nontrivial zero. In particular, if F is a local field, then 2t^2+3 variables insure the existence of a nontrivial zero (2t^2+1 if t is even), while if F=Q_p with p>=11, then 2t^2-2t+5 variables suffice (2t^2-2t+1 if 3 divides t). The improvement lies in a more efficient use of information on the solubility of pairs and triplets of quadratic forms, and the arguments are completely elementary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-04-08T20:51:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D72"
    ],
    "keywords": [
      "quadratic forms",
      "solubility",
      "nontrivial zero",
      "variables insure",
      "local field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......4051M"
    }
  }
}