{
  "id": "1608.05697",
  "version": "v1",
  "published": "2016-08-19T19:02:12.000Z",
  "updated": "2016-08-19T19:02:12.000Z",
  "title": "The number of $\\mathbb{F}_p$-points on Dwork hypersurfaces and hypergeometric functions",
  "authors": [
    "Dermot McCarthy"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We provide a formula for the number of $\\mathbb{F}_{p}$-points on the Dwork hypersurface $$x_1^n + x_2^n \\dots + x_n^n - n \\lambda \\, x_1 x_2 \\dots x_n=0$$ in terms of a $p$-adic hypergeometric function previously defined by the author. This formula holds in the general case, i.e for any $n, \\lambda \\in \\mathbb{F}_p^{*}$ and for all odd primes $p$, thus extending results of Goodson and Barman et al which hold in certain special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-19T19:02:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dwork hypersurface",
      "adic hypergeometric function",
      "special cases",
      "odd primes",
      "general case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}