{
  "id": "1909.10294",
  "version": "v1",
  "published": "2019-09-23T11:23:45.000Z",
  "updated": "2019-09-23T11:23:45.000Z",
  "title": "A family of $q$-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial",
  "authors": [
    "Victor J. W. Guo",
    "Michael J. Schlosser"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove a two-parameter family of $q$-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Crucial ingredients in our proof are George Andrews' multiseries extension of the Watson transformation, and a Karlsson--Minton type summation for very-well-poised basic hypergeometric series due to George Gasper. The new family of $q$-congruences is then used to prove two conjectures posed earlier by the authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-23T11:23:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "11A07",
      "11B65"
    ],
    "keywords": [
      "hypergeometric congruences modulo",
      "fourth power",
      "cyclotomic polynomial",
      "karlsson-minton type summation",
      "very-well-poised basic hypergeometric series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}