{
  "abstract": "We study Shimoda's theorem on the holomorphicity of a function $f(z,w)$ defined in a bidisc $U\\times V=\\left\\{ \\left| z \\right|<1 \\right\\}\\times \\left\\{ \\left| w \\right|<1 \\right\\},$ which is holomorphic with respect to $w\\in V$ for each fixed $z\\in U$ and is holomorphic with respect to $z\\in U$ for each fixed $w\\in E$, where $E\\subset V$ is a countable set with at least one limit point in $V$. Shimoda proved that in this case $f(z,w)$ is holomorphic in $U\\times V$ except for a nowhere dense closed subset of $U\\times V$. We prove a converse: for any relatively closed nowhere dense set $S\\subset U$ such that $\\partial U\\bigcup S$ is connected, there exists a function satisfying the conditions of Shimoda's theorem that is holomorphic in $(U\\setminus S)\\times V$ and doesn't extend holomorphically to any point of $S\\times V$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40381",
  "author_total": 2,
  "authors": [
    {
      "name": "Sevdiyor Imomkulov"
    },
    {
      "name": "Kamol Rasulov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgb790xsqtbmz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40381",
  "fulltext_url": null,
  "id": "dgb790xsqtbmz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40381",
  "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/2610.40381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgb790xsqtbmz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40381"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the Converse of Shimoda's Theorem",
  "title_text": "On the Converse of Shimoda's Theorem",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:51Z",
  "url": "https://research.draconitic.com/paper/dgb790xsqtbmz",
  "venue": "arXiv",
  "versions": []
}