{
  "abstract": "For a meromorphic function $f$ in the complex plane, we determine when $f$ and $f^{(k)}$ are algebraically dependent. This happens precisely when $f$ belongs to the class $W$ of elliptic functions and their degenerates, or satisfies a linear differential equation $f^{(k)} + af + b = 0$ with constant coefficients. The case of functions having a pole was settled previously. We complete the proof by treating entire solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20438",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexandre Eremenko"
    },
    {
      "name": "Tuen Wai Ng"
    },
    {
      "name": "Teng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b8vp1q1zn3x55.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20438",
  "fulltext_url": null,
  "id": "b8vp1q1zn3x55",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20438",
  "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.CA"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2604|Meromorphic and Entire Functions"
    ]
  ],
  "openalex": "W7221927987",
  "pdf_url": "https://arxiv.org/pdf/2610.20438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8vp1q1zn3x55.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Entire solutions of higher order Briot-Bouquet equations",
  "title_text": "Entire solutions of higher order Briot-Bouquet equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/b8vp1q1zn3x55",
  "venue": "arXiv",
  "versions": []
}