{
  "id": "1101.0983",
  "version": "v2",
  "published": "2011-01-05T14:14:32.000Z",
  "updated": "2012-04-01T10:16:37.000Z",
  "title": "Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials",
  "authors": [
    "Victor J. W. Guo",
    "Jiang Zeng"
  ],
  "comment": "11 pages, to appear in Journal of Number Theory",
  "journal": "J. Number Theory 132, 1731-1740 (2012)",
  "doi": "10.1016/j.jnt.2012.02.004",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "The Apery polynomials are defined by $A_n(x)=\\sum_{k=0}^{n}{n\\choose k}^2{n+k\\choose k}^2 x^k$ for all nonnegative integers $n$. We confirm several conjectures of Z.-W. Sun on the congruences for the sum $\\sum_{k=0}^{n-1}(-1)^k(2k+1) A_k(x)$ with $x\\in Z$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-01T10:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11B65",
      "05A10",
      "05A19"
    ],
    "keywords": [
      "apery polynomials",
      "congruences",
      "conjectures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.0983G"
    }
  }
}