{
  "id": "2101.09753",
  "version": "v1",
  "published": "2021-01-24T17:00:25.000Z",
  "updated": "2021-01-24T17:00:25.000Z",
  "title": "Some $q$-supercongruences modulo the square and cube of a cyclotomic polynomial",
  "authors": [
    "Victor J. W. Guo",
    "Michael J. Schlosser"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Two $q$-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two $q$-supercongruences that were earlier conjectured by the same authors and involve $q$-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved $q$-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-24T17:00:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "11A07",
      "11B65"
    ],
    "keywords": [
      "cyclotomic polynomial",
      "supercongruences modulo",
      "truncated basic hypergeometric series containing",
      "fourth power",
      "hold modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}