{
  "id": "1902.03851",
  "version": "v1",
  "published": "2019-02-11T13:04:45.000Z",
  "updated": "2019-02-11T13:04:45.000Z",
  "title": "Congruences on sums of $q$-binomial coefficients",
  "authors": [
    "Ji-Cai Liu",
    "Fedor Petrov"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by Guo. We also deduce a $q$-analogue of a congruence due to Apagodu and Zeilberger from Guo's $q$-congruence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-11T13:04:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "11A07",
      "05A10"
    ],
    "keywords": [
      "binomial coefficients",
      "sun-zhaos congruence",
      "harmonic sums",
      "series identity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}