{
  "id": "math/0404456",
  "version": "v3",
  "published": "2004-04-26T07:46:53.000Z",
  "updated": "2005-03-18T16:10:42.000Z",
  "title": "Counting rational points on hypersurfaces",
  "authors": [
    "T. D. Browning",
    "D. R. Heath-Brown"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F(x_1,...,x_n)$ be a form of degree $d\\geq 2$, which produces a geometrically irreducible hypersurface in $\\mathbb{P}^{n-1}$. This paper is concerned with the number of rational points on F=0 which have height at most $B$. Whenever $n<6$, or whenever the hypersurface is not a union of lines, we obtain estimates that are essentially best possible and that are uniform in $d$ and $n$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-03-18T16:10:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35"
    ],
    "keywords": [
      "counting rational points",
      "geometrically irreducible hypersurface",
      "essentially best"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4456B"
    }
  }
}