{
  "abstract": "We prove a conjecture proposed by the first-named author in 1998. Let $f\\colon\\mathbb{C}\\to\\mathbb{P}^n$ be a transcendental linearly non-degenerate holomorphic curve of finite lower order. If the counting function $N_1(r,f)$ of its Wronskian zeros satisfies $N_1(r,f)=o(T(r,f))$, then its order and lower order coincide and belong to $\\{1+k/q:k\\in\\mathbb{Z}_{\\geq 0},\\ 2\\le q\\le n+1\\}$, and its characteristic is regularly varying. Every order in this set occurs. We also prove the sharp inequality $\\limsup_{r\\to\\infty}N_1(r,f)/T(r,f)\\geq 1$ for transcendental linearly non-degenerate curves of order zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38032",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexandre Eremenko"
    },
    {
      "name": "Teng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6cbm1wh7tv8qg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38032",
  "fulltext_url": null,
  "id": "6cbm1wh7tv8qg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38032",
  "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",
      "2604|Meromorphic and Entire Functions"
    ]
  ],
  "openalex": "W7214960557",
  "pdf_url": "https://arxiv.org/pdf/2609.38032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6cbm1wh7tv8qg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.38032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38032"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Holomorphic curves of finite lower order with few inflection points",
  "title_text": "Holomorphic curves of finite lower order with few inflection points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/6cbm1wh7tv8qg",
  "venue": "arXiv",
  "versions": []
}