{
  "abstract": "In this paper, we prove two conjectures concerning parametric $q$- supercongruences related to Van Hamme's $\\mathrm{(G.2)}$ supercongruence. First, we confirm Tang\\rq s conjecture \\cite[Conjecture $4.1$]{Tang G2} by establishing the corresponding congruences modulo $[m]Φ_m(q)^2$. Second, we prove a conjecture of Wang and Xu \\cite[Conjecture $2$]{WangXu24}, extending their $q$-supercongruence modulo $Φ_m(q)^5$ to modulo $[m]Φ_m(q)^4$ when $m\\equiv1\\pmod4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15050",
  "author_total": 2,
  "authors": [
    {
      "name": "Liton Karmakar"
    },
    {
      "name": "Arijit Jana"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bjzxzcj4yen1y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15050",
  "fulltext_url": null,
  "id": "bjzxzcj4yen1y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15050",
  "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": "W7221797973",
  "pdf_url": "https://arxiv.org/pdf/2610.15050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bjzxzcj4yen1y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Proof of Two Conjectural $q$-Supercongruences Related to Van Hamme's $\\mathrm{(G.2)}$ Supercongruence",
  "title_text": "Proof of Two Conjectural q-Supercongruences Related to Van Hamme's (G.2) Supercongruence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/bjzxzcj4yen1y",
  "venue": "arXiv",
  "versions": []
}