{
  "id": "1303.2729",
  "version": "v2",
  "published": "2013-03-12T00:15:39.000Z",
  "updated": "2013-05-23T18:58:41.000Z",
  "title": "A note on sumsets of subgroups in $\\mathbb Z_p^*$",
  "authors": [
    "Derrick Hart"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $A$ be a multiplicative subgroup of $\\mathbb Z_p^*$. Define the $k$-fold sumset of $A$ to be $kA=\\{x_1+\\dots+x_k:x_i \\in A,1\\leq i\\leq k\\}$. We show that $6A\\supseteq \\mathbb Z_p^*$ for $|A| > p^{\\frac {11}{23} +\\epsilon}$. In addition, we extend a result of Shkredov to show that $|2A|\\gg |A|^{\\frac 85-\\epsilon}$ for $|A|\\ll p^{\\frac 59}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-23T18:58:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fold sumset",
      "multiplicative subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.2729H"
    }
  }
}