{
  "id": "2005.02998",
  "version": "v1",
  "published": "2020-05-06T17:58:40.000Z",
  "updated": "2020-05-06T17:58:40.000Z",
  "title": "Schinzel Hypothesis with probability 1 and rational points",
  "authors": [
    "Alexei N. Skorobogatov",
    "Efthymios Sofos"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove the existence version of Schinzel's Hypothesis (H) for $100\\%$ of integer polynomials $P_1, \\ldots, P_n$ of fixed degrees, when ordered by the size of coefficients. We deduce that a positive proportion of diagonal conic bundles over $\\mathbb{Q}$ with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Ch\\^atelet equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-06T17:58:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N32",
      "14G05"
    ],
    "keywords": [
      "rational point",
      "schinzel hypothesis",
      "probability",
      "diagonal conic bundles",
      "integer polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}