{
  "abstract": "In the paper, using Nevanlinna's value distribution theory of meromorphic functions in $\\mathbb{C}^m$, we study the problem: Let $f$ and $g$ be two finite order non-constant meromorphic functions in $\\mathbb{C}^m$ such that $f$ and $g$ share $0$ and $\\infty$ CM. If $\\partial_{z_i}(f)$ and $\\partial_{z_i}(g)$ share $0$ CM and if for one $n>1$, $\\partial^n_{z_i}(f)$ and $\\partial^n_{z_i}(g)$ share $0$ CM, where $i=1,2,\\ldots,m$, then $f$ and $g$ have special presentations. Our finding extends the result of Köhler (Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros, Complex Var., 11 (1989), 39-48) into higher dimensions. Moreover, we show by an example that the restriction on the growth of $f$ and $g$ is necessary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02682",
  "author_total": 3,
  "authors": [
    {
      "name": "Hong Yan Xu"
    },
    {
      "name": "Sujoy Majumder"
    },
    {
      "name": "Goutam Haldar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43xch5cbssbj3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02682",
  "fulltext_url": null,
  "id": "43xch5cbssbj3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02682",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02682",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43xch5cbssbj3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02682",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02682"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Meromorphic functions together with their partial derivatives sharing zeros and poles in $\\mathbb{C}^m$",
  "title_text": "Meromorphic functions together with their partial derivatives sharing zeros and poles in ℂ^m",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/43xch5cbssbj3",
  "venue": "arXiv",
  "versions": []
}