{
  "id": "math/0405475",
  "version": "v1",
  "published": "2004-05-25T04:29:09.000Z",
  "updated": "2004-05-25T04:29:09.000Z",
  "title": "A New Proof of Hilbert's Theorem on Ternary Quartics",
  "authors": [
    "Victoria Powers",
    "Bruce Reznick",
    "Claus Scheiderer",
    "Frank Sottile"
  ],
  "comment": "4 pages",
  "journal": "Comptes Rendus Mathematique (Paris), 339, Issue 9, (2004), 617--620.",
  "categories": [
    "math.AG"
  ],
  "abstract": "David Hilbert proved that a non-negative real quartic form f(x,y,z) is the sum of three squares of quadratic forms. We give a new proof which shows that if the complex plane curve Q defined by f is smooth, then f has exactly 8 such representations, up to equivalence. They correspond to those real 2-torsion points of the Jacobian of Q which are not represented by a conjugation-invariant divisor on Q.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-25T04:29:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E25",
      "14F22"
    ],
    "keywords": [
      "ternary quartics",
      "hilberts theorem",
      "non-negative real quartic form",
      "complex plane curve",
      "quadratic forms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5475P"
    }
  }
}