{
  "abstract": "Recently, Jana and Kalita (Res. Number Theory $\\textbf{8}~ (2022),$ Article $54$) obtained certain supercongruences motivated by some generalized Van Hamme type supercongruences, specifically for an integer $\\ell \\geq 2$ and an odd prime $p$ with $p \\equiv -1 \\pmod{\\ell},$ \\begin{align*} \\displaystyle \\sum_{n=0}^{\\frac{p^v + 1}{\\ell}} (-1)^n (2 \\ell n - 1) (\\ell^2 n^2 - \\ell n + 1) \\frac{(-\\frac{1}{\\ell})_n^3}{(1)_n^3} \\equiv (-1)^{\\frac{p^v + p + 2}{\\ell}} p^{3v} \\pmod{p^{3v+1}}, \\end{align*} and \\begin{align*} \\displaystyle \\sum_{n=0}^{\\frac{p^v + 1}{\\ell}} (2 \\ell n - 1) (2 \\ell^2 n^2 - 2 \\ell n + 1) \\frac{(-\\frac{1}{\\ell})_n^4}{(1)_n^4} \\equiv - p^{4v} \\pmod{p^{4v+1}}. \\end{align*} Employing the $q$-telescoping technique, similar to the $q$-WZ method, we here establish some supercongruences involving certain $q$-shifted factorials. As particular cases, we provide $q$-analogues of the above supercongruences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29071",
  "author_total": 1,
  "authors": [
    {
      "name": "Liton Karmakar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2sr1an330tms.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29071",
  "fulltext_url": null,
  "id": "b2sr1an330tms",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29071",
  "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": "W7204917183",
  "pdf_url": "https://arxiv.org/pdf/2608.29071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2sr1an330tms.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29071"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$q$-Analogues of some supercongruences related to generalized Van Hamme-type supercongruences",
  "title_text": "q-Analogues of some supercongruences related to generalized Van Hamme-type supercongruences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/b2sr1an330tms",
  "venue": "arXiv",
  "versions": []
}