{
  "id": "math/0505186",
  "version": "v3",
  "published": "2005-05-10T15:51:57.000Z",
  "updated": "2005-11-21T12:55:04.000Z",
  "title": "The density of rational points on non-singular hypersurfaces, II",
  "authors": [
    "T. D. Browning",
    "D. R. Heath-Brown"
  ],
  "comment": "36 pages; appendix by J. Starr",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "This paper establishes the conjecture that a non-singular projective hypersurface of dimension $r$, which is not equal to a linear space, contains $O(B^{r+\\epsilon})$ rational points of height at most $B$, for any choice of $\\epsilon>0$. The implied constant in this estimate depends at most upon $\\epsilon, r$ and the degree of the hypersurface.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-11-21T12:55:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "11G35",
      "14G05"
    ],
    "keywords": [
      "rational points",
      "non-singular hypersurfaces",
      "estimate depends",
      "non-singular projective hypersurface",
      "linear space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5186B"
    }
  }
}