{
  "abstract": "We study the Shimura curves $X_D^*(1)$ of discriminant $D$ for $D=14, 15$ relating specific weight $4$ modular forms on these Shimura curves to the associated Heun functions for the quadrilateral group. We also discuss how the Picard-Fuchs equation of the associated family of abelian surfaces has solutions coming from modular forms on $X^*_{D}(1)$. We determine the rational exceptional sets of the associated Heun functions, and the algebraic values attained by the Heun function at these points. For example, $${\\rm He}\\left( 81, \\frac{1}{2}; \\frac{1}{3}, \\frac{1}{6}, \\frac{1}{2}, \\frac{1}{2};-\\frac{729}{112}\\right)= \\left( \\frac{2^2 \\cdot 3^3 \\cdot 5^3}{7^5} \\right)^{\\frac{1}{6}} $$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14495",
  "author_total": 2,
  "authors": [
    {
      "name": "Harshavardhan Reddy"
    },
    {
      "name": "Devendra Tiwari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90syggm6xx9n1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14495",
  "fulltext_url": null,
  "id": "90syggm6xx9n1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14495",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7203597425",
  "pdf_url": "https://arxiv.org/pdf/2608.14495",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90syggm6xx9n1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2608.14495",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14495"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Shimura curves of discriminant 14 and 15 and associated Heun Functions",
  "title_text": "Shimura curves of discriminant 14 and 15 and associated Heun Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/90syggm6xx9n1",
  "venue": "arXiv",
  "versions": []
}