{
  "id": "0806.1040",
  "version": "v3",
  "published": "2008-06-05T19:24:27.000Z",
  "updated": "2008-06-23T04:31:59.000Z",
  "title": "An upper bound on the multiplicative energy",
  "authors": [
    "Jozsef Solymosi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the sumset or the productset of any finite set of real numbers, $A,$ is at least $|A|^{4/3-\\epsilon},$ improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy, $E(A,A).$",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-06-23T04:31:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R05",
      "11B75"
    ],
    "keywords": [
      "upper bound",
      "multiplicative energy",
      "main tool",
      "real numbers",
      "improving earlier bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1040S"
    }
  }
}