{
  "id": "1801.03082",
  "version": "v1",
  "published": "2018-01-09T18:52:44.000Z",
  "updated": "2018-01-09T18:52:44.000Z",
  "title": "Prime and square-free values of polynomials in moderately many variables",
  "authors": [
    "Kevin Destagnol",
    "Efthymios Sofos"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study prime values of irreducible polynomials in many variables. The method uses the arguments behind Birch's well-known result regarding the Hasse principle for complete intersections, however, we prove our results in $50\\%$ fewer variables than in the Birch setting. As an application, we derive the Hasse principle and weak approximation for pencils of certain varieties in the spirit of work by Colliot-Th\\'el\\`ene-Sansuc and Harpaz-Skorobogatov-Wittenberg. We also study the problem of square-free values of an integer polynomial with 66.6\\% fewer variables than in the Birch setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-09T18:52:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N32",
      "11P55",
      "14G05"
    ],
    "keywords": [
      "square-free values",
      "fewer variables",
      "hasse principle",
      "study prime values",
      "birchs well-known result regarding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}