{
  "id": "math/0703676",
  "version": "v1",
  "published": "2007-03-22T18:17:12.000Z",
  "updated": "2007-03-22T18:17:12.000Z",
  "title": "Garaev's Inequality in finite fields not of prime order",
  "authors": [
    "Nets Hawk Katz",
    "Chun-Yen Shen"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We prove a version of Garaev's sum product theorem in the set of finite fields with non-prime order. Because of the presence of subfields, this seems to require some hypotheses on the set. We work under a condition analogous to having Hausdorff dimension less than 1/2. Under these conditions, we obtain a sum-product theorem with exponent 49/48.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-22T18:17:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T99",
      "05D99"
    ],
    "keywords": [
      "finite fields",
      "garaevs inequality",
      "garaevs sum product theorem",
      "sum-product theorem",
      "non-prime order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3676H"
    }
  }
}