{
  "id": "1507.07391",
  "version": "v1",
  "published": "2015-07-27T12:57:34.000Z",
  "updated": "2015-07-27T12:57:34.000Z",
  "title": "Supercongruences for truncated hypergeometric series and p-adic gamma function",
  "authors": [
    "Rupam Barman",
    "Neelam Saikia"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove several supercongruences for truncated hypergeometric series and $p$-adic Gamma function. Recently, A. Deines, J. Fuselier, L. Long, H. Swisher and F. Tu posed some open problems on supercongruences in \\cite{DFLST} based on numeric observations. We prove two of the supercongruences posed in \\cite{DFLST}. Our results also generalize certain supercongruences proved in \\cite{DFLST}. One of our supercongruence is similar to a supercongruence proved by L. Long and R. Ramakrishna in \\cite{long}. The supercongruence conjectured by Rodriguez-Villegas and proved by E. Mortenson \\cite{mortenson2} using the theory of Gaussian hypergeometric series follows from one of our more general supercongruence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-27T12:57:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E50",
      "33C20",
      "33C99",
      "11S80"
    ],
    "keywords": [
      "truncated hypergeometric series",
      "p-adic gamma function",
      "gaussian hypergeometric series",
      "numeric observations",
      "general supercongruence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150707391B"
    }
  }
}