{
  "id": "math/0506497",
  "version": "v1",
  "published": "2005-06-24T09:33:57.000Z",
  "updated": "2005-06-24T09:33:57.000Z",
  "title": "Plane curves in boxes and equal sums of two powers",
  "authors": [
    "T. D. Browning",
    "D. R. Heath-Brown"
  ],
  "comment": "15 pages; to appear in Math. Zeit",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given an absolutely irreducible ternary form $F$, the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are restricted to lie in very lopsided boxes. As an application of the main result, a new paucity estimate is obtained for equal sums of two like powers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-24T09:33:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "11P05"
    ],
    "keywords": [
      "equal sums",
      "plane curves",
      "produce better upper bounds",
      "paucity estimate",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6497B"
    }
  }
}