{
  "abstract": "We provide an explicit analytical evaluation of Ramanujan-type series for $1/π$. Focusing on the singular moduli $k_{r}$ for $r \\in \\{5, 7, 13, 37\\}$, we demonstrate that the underlying elliptic identities can be established through lower-degree modular transformations. Specifically, we resolve the case $r = 5$ via a combination of degree-2 and degree-3 modular transformations; the case $r = 7$ utilizing the modular transformation of degree 2; the case $r = 13$ via a combination of degree-2 and degree-7 modular transformations; and the case $r = 37$ via a combination of degree-2 and degree-19 modular transformations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11924",
  "author_total": 1,
  "authors": [
    {
      "name": "Pablo Fernández Refolio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6pdgm19gn8dxq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11924",
  "fulltext_url": null,
  "id": "6pdgm19gn8dxq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11924",
  "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": "W7168354229",
  "pdf_url": "https://arxiv.org/pdf/2607.11924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6pdgm19gn8dxq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2607.11924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Advanced Mathematical Identities",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Analytical Evaluation of Ramanujan Series for $1/π$ via Degree-2, Degree-3, Degree-7, and Degree-19 Modular Transformations",
  "title_text": "Analytical Evaluation of Ramanujan Series for 1/π via Degree-2, Degree-3, Degree-7, and Degree-19 Modular Transformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/6pdgm19gn8dxq",
  "venue": "arXiv",
  "versions": []
}