{
  "id": "1106.1148",
  "version": "v1",
  "published": "2011-05-31T10:04:52.000Z",
  "updated": "2011-05-31T10:04:52.000Z",
  "title": "An improved sum-product estimate over finite fields",
  "authors": [
    "Liangpan Li",
    "Oliver Roche-Newton"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper gives an improved sum-product estimate for subsets of a finite field whose order is not prime. It is shown, under certain conditions, that $$\\max\\{|A+A|,|A\\cdot{A}|\\}\\gg{\\frac{|A|^{12/11}}{(\\log_2|A|)^{5/11}}}.$$ This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev (\\cite{mishaSP}).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-31T10:04:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "sum-product estimate",
      "estimate matches",
      "prime fields",
      "logarithmic factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1148L"
    }
  }
}