{
  "id": "1401.0233",
  "version": "v1",
  "published": "2014-01-01T00:05:55.000Z",
  "updated": "2014-01-01T00:05:55.000Z",
  "title": "A positive proportion of elliptic curves over $\\mathbb{Q}$ have rank one",
  "authors": [
    "Manjul Bhargava",
    "Christopher Skinner"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that, when all elliptic curves over $\\mathbb{Q}$ are ordered by naive height, a positive proportion have both algebraic and analytic rank one. It follows that the average rank and the average analytic rank of elliptic curves are both strictly positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-01T00:05:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11R45"
    ],
    "keywords": [
      "elliptic curves",
      "positive proportion",
      "average analytic rank",
      "average rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0233B"
    }
  }
}