{
  "id": "math/0609426",
  "version": "v3",
  "published": "2006-09-14T23:44:11.000Z",
  "updated": "2006-10-15T09:14:47.000Z",
  "title": "Sum-product estimates in finite fields",
  "authors": [
    "D. Hart",
    "A. Iosevich",
    "J. Solymosi"
  ],
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "We prove, using combinatorics and Kloosterman sum technology that if $A \\subset {\\Bbb F}_q$, a finite field with $q$ elements, and $q^{{1/2}} \\lesssim |A| \\lesssim q^{{7/10}}$, then $\\max \\{|A+A|, |A \\cdot A|\\} \\gtrsim \\frac{{|A|}^{{3/2}}}{q^{{1/4}}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-10-15T09:14:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "sum-product estimates",
      "kloosterman sum technology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9426H"
    }
  }
}