{
  "id": "1810.12791",
  "version": "v1",
  "published": "2018-10-30T14:57:48.000Z",
  "updated": "2018-10-30T14:57:48.000Z",
  "title": "Logarithmic bounds for Roth's theorem via almost-periodicity",
  "authors": [
    "Thomas F. Bloom",
    "Olof Sisask"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if $A \\subset \\{1,2,\\ldots,N\\}$ is free of three-term progressions, then $\\lvert A\\rvert \\leq N/(\\log N)^{1-o(1)}$. Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-30T14:57:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B30",
      "11K70",
      "28C10"
    ],
    "keywords": [
      "roths theorem",
      "logarithmic bounds",
      "almost-periodicity",
      "arithmetic progressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}