{
  "abstract": "We disprove a conjecture of Ruscheweyh, Salinas and Sugawa concerning the universal convexity of the normalized generating function associated with the Ramanujan sequence $θ(n).$ More precisely, we prove that the function \\[ σ(z)=\\frac{1}{θ(1)-1/3}\\sum_{n\\geq1}(θ(n)-1/3)z^{n} \\] is not universally convex on the slit domain $\\mathbb{C}\\backslash[1,\\infty).$ The proof uses Watson\\textquoteright s integral representation of $θ(n),$ asymptotic estimates for an auxiliary function $h,$ and the representation of derivatives of universally convex functions via logarithmic integrals. As a general extension of this result, we also show that the generalized Ramanujan generating function \\[ σ_α(z)=\\frac{1}{θ(1)-1/3}\\sum_{n\\geq1}(θ(n)-1/3)\\frac{z^{n}}{n^α} \\] is universally convex if and only if $α\\geq1.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07479",
  "author_total": 1,
  "authors": [
    {
      "name": "Bing He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3as79tdwvxkd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07479",
  "fulltext_url": null,
  "id": "f3as79tdwvxkd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07479",
  "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.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3as79tdwvxkd.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Disproof of a conjecture of Ruscheweyh et al. on universal convexity of Ramanujan generating function",
  "title_text": "Disproof of a conjecture of Ruscheweyh et al. on universal convexity of Ramanujan generating function",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:21Z",
  "url": "https://research.draconitic.com/paper/f3as79tdwvxkd",
  "venue": "arXiv",
  "versions": []
}