{
  "id": "1104.3047",
  "version": "v2",
  "published": "2011-04-15T13:16:27.000Z",
  "updated": "2011-04-18T12:47:27.000Z",
  "title": "Congruences involving $\\binom{2k}k^2\\binom{4k}{2k}m^{-k}$",
  "authors": [
    "Zhi-Hong Sun"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $p>3$ be a prime, and let $m$ be an integer with $p\\nmid m$. In the paper, by using the work of Ishii and Deuring's theorem for elliptic curves with complex multiplication we solve some conjectures of Zhi-Wei Sun concerning $\\sum_{k=0}^{p-1}\\binom{2k}k^2\\binom{4k}{2k}m^{-k}\\mod {p^2}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-18T12:47:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "33C45",
      "11E25",
      "11G07",
      "11L10",
      "05A10",
      "05A19"
    ],
    "keywords": [
      "congruences",
      "elliptic curves",
      "complex multiplication",
      "deurings theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.3047S"
    }
  }
}