{
  "id": "1304.3321",
  "version": "v2",
  "published": "2013-04-11T14:32:49.000Z",
  "updated": "2013-11-20T06:04:28.000Z",
  "title": "p-adic Gamma function and traces of Frobenius of elliptic curves",
  "authors": [
    "Rupam Barman",
    "Neelam Saikia"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In \\cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\\cdots]$ using Teichm\\\"{u}ller character of finite fields and quotients of $p$-adic gamma function, and expressed the trace of Frobenius of elliptic curves in terms of special values of $_{2}G_{2}[\\cdots]$. We establish two different expressions for the traces of Frobenius of elliptic curves in terms of the function $_{2}G_{2}[\\cdots]$. As a result, we obtain two relations between special values of the function $_{2}G_{2}[\\cdots]$ with different parameters.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-20T06:04:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "33E50",
      "33C99",
      "11S80",
      "11T24"
    ],
    "keywords": [
      "elliptic curves",
      "p-adic gamma function",
      "special values",
      "finite fields",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.3321B"
    }
  }
}