{
  "id": "2410.14149",
  "version": "v1",
  "published": "2024-10-18T03:38:01.000Z",
  "updated": "2024-10-18T03:38:01.000Z",
  "title": "A remark on modular equations involving Rogers-Ramanujan continued fraction via $5$-dissections",
  "authors": [
    "Russelle Guadalupe"
  ],
  "comment": "8 pages; comments welcome",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper, we study the $5$-dissections of certain Ramanujan's theta functions, particularly $\\psi(q)\\psi(q^2), \\varphi(-q)$ and $\\varphi(-q)\\varphi(-q^2)$, and derive an identity for $q(q;q)_{\\infty}^6/(q^5;q^5)_{\\infty}^6$ in terms of certain products of the Rogers-Ramanujan continued fraction $R(q)$. Using this identity, we give another proof of the modular equation involving $R(q), R(q^2)$ and $R(q^4)$, which was recorded by Ramanujan in his lost notebook, and establish modular equations involving $R(q), R(q^2), R(q^4), R(q^8)$ and $R(q^{16})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-18T03:38:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "05A30",
      "14K25",
      "33D15"
    ],
    "keywords": [
      "rogers-ramanujan continued fraction",
      "dissections",
      "ramanujans theta functions",
      "establish modular equations",
      "lost notebook"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}