{
  "abstract": "With the help of a summation formula for $q$-series and the creative microscoping method, we shall establish two parametric $q$-supercongruences. They are both modulo the third power of a cyclotomic polynomial. When $q\\to1$, one of them is able to engender the following conclusion: for any prime $p\\equiv2\\pmod{3}$ and any nonnegative integer $s$ subject to $ s\\leq (p-2)/3$, \\[\\sum_{k=s}^{(p+1)/3+s}(6k-1)\\frac{(-\\frac{1}{3})_{k-s}(-\\frac{1}{3})_{k+s}(-\\frac{1}{3})_{k}}{(k-s)!(k+s)!k!} \\equiv 0\\pmod{p^3}.\\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29986",
  "author_total": 2,
  "authors": [
    {
      "name": "Chuanan Wei"
    },
    {
      "name": "Guozhu Ruan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ntqcary622q5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29986",
  "fulltext_url": null,
  "id": "5ntqcary622q5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29986",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214276392",
  "pdf_url": "https://arxiv.org/pdf/2609.29986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ntqcary622q5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Two parametric q-supercongruences from a summation formula for q-series",
  "title_text": "Two parametric q-supercongruences from a summation formula for q-series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5ntqcary622q5",
  "venue": "arXiv",
  "versions": []
}