{
  "abstract": "Consider the Dirichlet-type spaces on the bidisc defined by $$\\mathcal{D}_β(\\mathbb{D}^2)=\\Bigg\\{f(z_1,z_2)=\\sum_{k,l}a_{kl}z_1^kz_2^l\\in\\mathcal{O}(\\mathbb{D}^2): \\sum_{k,l\\ge 0}|a_{kl}|^2(k+l+1)^β<+\\infty\\Bigg\\}.$$ Given $β_c\\in(0,2],$ we construct a function $f$ that belongs to the Dirichlet-type space $\\mathcal D_{2}(\\mathbb{D}^2)$ of the bidisk and is cyclic in $\\mathcal D_β(\\mathbb{D}^2)$ if and only if $β\\leq β_{c}.$ We also show that the critical index satisfies $β_c=2-\\mathrm{dim}_H(\\mathcal{Z}(f)\\cap \\mathbb{T}^2),$ where $\\mathrm{dim_H}(\\mathcal{Z}(f)\\cap \\mathbb{T}^2)$ is the Hausdorff dimension of the zero set of the function $f$ on the two-torus $\\mathbb{T}^2.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09952",
  "author_total": 2,
  "authors": [
    {
      "name": "Athanasios Beslikas"
    },
    {
      "name": "Pouriya Torkinejad Ziarati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78pysbd6z6345.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09952",
  "fulltext_url": null,
  "id": "78pysbd6z6345",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09952",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7212111733",
  "pdf_url": "https://arxiv.org/pdf/2609.09952",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78pysbd6z6345.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.09952",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09952"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Critical cyclicity in Dirichlet-type spaces on the bidisk",
  "title_text": "Critical cyclicity in Dirichlet-type spaces on the bidisk",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/78pysbd6z6345",
  "venue": "arXiv",
  "versions": []
}