{
  "abstract": "Recently, Guo and Guo (Results Math $76:37, ~2021$) obtained curious $q$-analogues of the following two supercongruences conjectured by Guo and Schlosser \\cite[Conjectures $12.6$ and $12.7$]{GuoSclssr ConstApprox 21}: \\begin{align*} \\sum_{n=0}^{(p-1)/3} (6n+1) \\frac{\\left(\\frac{1}{3}\\right)_n^{4}(2n)!} {(n!)^{4}\\left(\\frac{2}{3}\\right)_{2n}} \\equiv p \\pmod{p^{3}} \\qquad \\text{for primes } p\\equiv 1 \\pmod{3}, \\end{align*} \\begin{align*} \\sum_{n=0}^{(p+1)/3} (6n-1) \\frac{\\left(-\\frac{1}{3}\\right)_n^{4}(2n)!} {(n!)^{4}\\left(-\\frac{2}{3}\\right)_{2n}} \\equiv p \\pmod{p^{3}} \\qquad \\text{for primes } p\\equiv 2 \\pmod{3}, \\end{align*} where $(z)_n=z(z+1)\\cdots(z+n-1)$ denotes the shifted factorial. In this paper, we establish a one-parameter extension of them. The main ingredients of our proofs are the creative microscoping method developed by Guo and Zudilin \\cite{guo2019q} and Andrews' multi-series transformation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33249",
  "author_total": 1,
  "authors": [
    {
      "name": "Liton Karmakar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2240w76h19tzm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33249",
  "fulltext_url": null,
  "id": "2240w76h19tzm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33249",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7223833769",
  "pdf_url": "https://arxiv.org/pdf/2610.33249",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2240w76h19tzm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33249",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33249"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Two parametric $q$-supercongruences from Andrews' multi-series transformation",
  "title_text": "Two parametric q-supercongruences from Andrews' multi-series transformation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2240w76h19tzm",
  "venue": "arXiv",
  "versions": []
}