{
  "id": "1311.5252",
  "version": "v2",
  "published": "2013-11-20T22:34:03.000Z",
  "updated": "2015-08-04T21:20:34.000Z",
  "title": "On the $p$-integrality of $A$-hypergeometric series",
  "authors": [
    "Alan Adolphson",
    "Steven Sperber"
  ],
  "comment": "Expanded introduction, Sections 2 and 5 rewritten, Section 7 added, small changes elsewhere",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $A$ be a set of $N$ vectors in ${\\mathbb Z}^n$ and let $v$ be a vector in ${\\mathbb C}^N$ that has minimal negative support for $A$. Such a vector $v$ gives rise to a formal series solution of the $A$-hypergeometric system with parameter $\\beta = Av$. If $v$ lies in ${\\mathbb Q}^n$, then this series has rational coefficients. Let $p$ be a prime number. We characterize those $v$ whose coordinates are rational, $p$-integral, and lie in the closed interval $[-1,0]$ for which the corresponding normalized series solution has $p$-integral coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-20T22:34:03.000Z",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-04T21:20:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypergeometric series",
      "integrality",
      "formal series solution",
      "minimal negative support",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.5252A"
    }
  }
}