{
  "abstract": "In this paper, we explicitly determine an algebraic Belyi function on a unique smooth projective model $\\widetilde{W}$ of the Wiman sextic curve $W$ and describe its complex uniformization in terms of modular functions associated with a certain noncongruence subgroup $Γ_{\\widetilde{W}} \\subset {\\rm SL}_2(\\mathbb{Z})$. As an application, we give a direct proof of the unbounded denominators conjecture for weight $2$ cusp forms with respect to $Γ_{\\widetilde{W}}$. The conjecture is now known in full generality by the work of Calegari, Dimitrov, and Tang, following earlier progress including work of Dong, Lin, and Ng. Our proof, however, uses a degeneration of $\\widetilde{W}$ over $\\mathbb{F}_{5}$ together with explicit Puiseux series expansions and is substantially different from the methods employed in their work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30798",
  "author_total": 2,
  "authors": [
    {
      "name": "Madoka Horie"
    },
    {
      "name": "Takuya Yamauchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28bhyfbm74hyz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30798",
  "fulltext_url": null,
  "id": "28bhyfbm74hyz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30798",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204954282",
  "pdf_url": "https://arxiv.org/pdf/2608.30798",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28bhyfbm74hyz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2608.30798",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30798"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An Explicit Belyi Map for the Wiman Sextic and Cusp Forms for a Noncongruence Subgroup",
  "title_text": "An Explicit Belyi Map for the Wiman Sextic and Cusp Forms for a Noncongruence Subgroup",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/28bhyfbm74hyz",
  "venue": "arXiv",
  "versions": []
}