{
  "id": "0708.4354",
  "version": "v3",
  "published": "2007-08-31T14:23:58.000Z",
  "updated": "2008-11-12T14:49:46.000Z",
  "title": "G-functions and multisum versus holonomic sequences",
  "authors": [
    "Stavros Garoufalidis"
  ],
  "comment": "8 pages, no figures",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "The purpose of the paper is three-fold: (a) we prove that every sequence which is a multidimensional sum of a balanced hypergeometric term has an asymptotic expansion of Gevrey type-1 with rational exponents, (b) we construct a class of $G$-functions that come from enumerative combinatorics, and (c) we give a counterexample to a question of Zeilberger that asks whether holonomic sequences can be written as multisums of balanced hypergeometric terms. The proofs utilize the notion of a $G$-function, introduced by Siegel, and its analytic/arithmetic properties shown recently by Andr\\'e.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-11-12T14:49:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M25"
    ],
    "keywords": [
      "holonomic sequences",
      "balanced hypergeometric term",
      "g-functions",
      "multidimensional sum",
      "asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.4354G"
    }
  }
}