{
  "id": "1005.1210",
  "version": "v2",
  "published": "2010-05-07T14:08:58.000Z",
  "updated": "2010-07-13T10:40:45.000Z",
  "title": "Arithmetic progressions in Salem-type subsets of the integers",
  "authors": [
    "Paul Potgieter"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a subset of the integers of zero density, we define the weaker notion of fractional density of such a set. It is shown how this notion corresponds to that of the Hausdorff dimension of a compact subset of the reals. We then show that a version of a theorem of {\\L}aba and Pramanik on 3-term arithmetic progressions in subsets of the unit interval also holds for subsets of the integers with fractional density and satisfying certain Fourier-decay conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-13T10:40:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B05",
      "11B25",
      "28A78",
      "26E35"
    ],
    "keywords": [
      "arithmetic progressions",
      "salem-type subsets",
      "fractional density",
      "notion corresponds",
      "unit interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1210P"
    }
  }
}