{
  "id": "0712.3882",
  "version": "v2",
  "published": "2007-12-22T22:13:13.000Z",
  "updated": "2008-01-11T00:46:02.000Z",
  "title": "Arithmetic progressions in sets of fractional dimension",
  "authors": [
    "Izabella Laba",
    "Malabika Pramanik"
  ],
  "comment": "42 pages",
  "journal": "Geom. Funct. Anal. 19 (2009), 429-456",
  "doi": "10.1007/s00039-009-0003-9",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "Let $E\\subset\\rr$ be a closed set of Hausdorff dimension $\\alpha$. We prove that if $\\alpha$ is sufficiently close to 1, and if $E$ supports a probabilistic measure obeying appropriate dimensionality and Fourier decay conditions, then $E$ contains non-trivial 3-term arithmetic progressions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-11T00:46:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "42A32",
      "42A38",
      "42A45",
      "11B25"
    ],
    "keywords": [
      "arithmetic progressions",
      "fractional dimension",
      "probabilistic measure obeying appropriate dimensionality",
      "fourier decay conditions",
      "hausdorff dimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3882L"
    }
  }
}