{
  "id": "0904.2075",
  "version": "v1",
  "published": "2009-04-14T09:19:46.000Z",
  "updated": "2009-04-14T09:19:46.000Z",
  "title": "Sum-product phenomena in F_p: a brief introduction",
  "authors": [
    "Ben Green"
  ],
  "comment": "10 pages, not for publication",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao theorem on the sum-product phenomenon in F_p. The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss. No originality is claimed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-14T09:19:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sum-product phenomenon",
      "brief introduction",
      "lent term",
      "simplest proof",
      "elon lindenstrauss"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2075G"
    }
  }
}