{
  "abstract": "We evaluate the six odd class-number-four cases left unevaluated in Ramanathan's treatment of the Rogers-Ramanujan continued fraction. Let \\[ S(q)=-R(-q),\\qquad R(q)=\\cfrac{q^{1/5}}{1+\\cfrac{q}{1+\\cfrac{q^2}{1+\\cfrac{q^3}{1+\\cdots}}}}. \\] For $n=39,87,111,119,159,287$ we determine the value of $S(e^{-π/\\sqrt{5n}})$ by applying the genus-character form of the Kronecker limit formula to the four ideal classes of $\\mathbb Q(\\sqrt{-5n})$. The resulting expressions are given in terms of fundamental units of real quadratic fields. In particular, if $X_n=S(e^{-π/\\sqrt{5n}})$, then \\[ X_n^{-5}+11-X_n^5=\\frac{5\\sqrt5}{U_n}, \\] where the six quantities $U_n$ are displayed explicitly below. We also give the corresponding radical expressions and quartic algebraic certificates, together with numerical checks of the six evaluations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10642",
  "author_total": 1,
  "authors": [
    {
      "name": "Sumit Kumar Jha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fz7289mxyz228.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10642",
  "fulltext_url": null,
  "id": "fz7289mxyz228",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10642",
  "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.GM"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7212257836",
  "pdf_url": "https://arxiv.org/pdf/2609.10642",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fz7289mxyz228.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10642",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10642"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Advanced Mathematical Identities",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Four-Genus Kronecker-Limit Evaluation of the Alternating Rogers-Ramanujan Continued Fraction",
  "title_text": "A Four-Genus Kronecker-Limit Evaluation of the Alternating Rogers-Ramanujan Continued Fraction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/fz7289mxyz228",
  "venue": "arXiv",
  "versions": []
}