{
  "abstract": "The primary objective of this paper is to determine the existence and explicit form of finite-order entire solutions in $\\mathbb{C}^n$ of the following system of Fermat-type partial differential-difference equations: \\[\\begin{cases} \\left(\\frac{\\partial f_1\\left(z\\right)}{\\partial z_1}\\right)^{n_1} + (f_2 \\left(z+c\\right)-f_1(z) )^{m_1}= 1, \\medskip \\left(\\frac{\\partial f_2\\left(z\\right)}{\\partial z_1}\\right)^{n_2} + (f_1 \\left(z+c \\right)-f_2(z) )^{m_2}= 1, \\end{cases}\\] for several choices of the positive integers $n_1$, $n_2$, $m_1$, and $m_2$, where $c=(c_1,c_2,\\ldots,c_n)$. We obtain structural classifications and nonexistence results in the exponent regimes specified in the main theorems, extending results of Xu et al. \\cite{XLL1} from $\\mathbb{C}^2$ to $\\mathbb{C}^n$. Several examples illustrate the resulting solution families.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.05240",
  "author_total": 4,
  "authors": [
    {
      "name": "Sujoy Majumder"
    },
    {
      "name": "Jhilik Banerjee"
    },
    {
      "name": "Abhijit Banerjee"
    },
    {
      "name": "Elias G. Saleeby"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5wrj17cr6pg9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.05240",
  "fulltext_url": null,
  "id": "5wrj17cr6pg9s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.05240",
  "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": "W7163682373",
  "pdf_url": "https://arxiv.org/pdf/2606.05240",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5wrj17cr6pg9s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.05240",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.05240"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-Order Entire Solutions to Fermat-Type Partial Differential-Difference Systems in $\\mathbb{C}^n$",
  "title_text": "Finite-Order Entire Solutions to Fermat-Type Partial Differential-Difference Systems in ℂ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/5wrj17cr6pg9s",
  "venue": "arXiv",
  "versions": []
}