{
  "abstract": "Let $χ$ be the quadratic Dirichlet character of conductor $N$ associated with a given real quadratic field $k$ and let $X_χ(N)$ be the double covering of $X_0(N)$ associated with $χ$. In this note, we study a modular unit $f$ on the curve $X_χ(N)$. We prove that the transform of $f$ by the Fricke involution $\\mathscr{w}_N$ is the level $N$ analogue of the Rogers-Ramanujan continued fraction introduced by Lee and Park. Furthermore, if $N$ is a positive prime discriminant, then $f$ is Ligozat's modular unit, which is known from Mazur's work on the Eisenstein ideal. We extend Ligozat's construction to any positive fundamental discriminant $N$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24307",
  "author_total": 1,
  "authors": [
    {
      "name": "Carlos Castano-Bernard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/648q7rrr6qaqk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24307",
  "fulltext_url": null,
  "id": "648q7rrr6qaqk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24307",
  "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": "W7223022855",
  "pdf_url": "https://arxiv.org/pdf/2610.24307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/648q7rrr6qaqk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Ramanujan-Ligozat modular unit",
  "title_text": "On the Ramanujan-Ligozat modular unit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/648q7rrr6qaqk",
  "venue": "arXiv",
  "versions": []
}