{
  "abstract": "For $a,b,c \\in \\mathbb{Q}$, the exceptional set associated to the Gauss hypergeometric function $_2F_1(a,b,c;z)$ is defined by $E(a,b,c) := \\{ z \\in \\overline{\\mathbb{Q}} \\mid {}_2F_1(a,b,c;z) \\in \\overline{\\mathbb{Q}} \\}.$ In this paper, the exceptional sets $E(a,b,c)$ are determined explicitly for each $_2F_1(a,b,c;z)$ whose monodromy group is an arithmetic triangle group in Takeuchi's class I. The description is obtained via hypergeometric-modular identities together with transcendence results for periods of abelian varieties due to Wüstholz, and classical result of Schneider on algebraic values of $j$-invariant of elliptic curves with complex multiplication.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.16331",
  "author_total": 1,
  "authors": [
    {
      "name": "Archisman Bhattacharjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19k296cz35caw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.16331",
  "fulltext_url": null,
  "id": "19k296cz35caw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.16331",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7169848152",
  "pdf_url": "https://arxiv.org/pdf/2607.16331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19k296cz35caw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2607.16331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.16331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions",
  "title_text": "Exceptional Sets for Certain _2F_1 Hypergeometric Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/19k296cz35caw",
  "venue": "arXiv",
  "versions": []
}