{
  "id": "1308.0060",
  "version": "v1",
  "published": "2013-07-31T22:55:30.000Z",
  "updated": "2013-07-31T22:55:30.000Z",
  "title": "Integral points on quadratic twists and linear growth for certain elliptic fibrations",
  "authors": [
    "Pierre Le Boudec"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove that the number of rational points of bounded height on certain del Pezzo surfaces of degree 1 defined over Q grows linearly, as predicted by Manin's conjecture. Along the way, we investigate the average number of integral points of small naive height on quadratic twists of a fixed elliptic curve with full rational 2-torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-31T22:55:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "11G05",
      "14G05"
    ],
    "keywords": [
      "integral points",
      "quadratic twists",
      "linear growth",
      "elliptic fibrations",
      "del pezzo surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0060L"
    }
  }
}