{
  "abstract": "We prove the dynamical uniform boundedness conjecture for unicritical polynomials $z^d + c$ over every number field $K$ when $d \\geq 4$, and over every number field $K$ not containing $\\mathbb{Q}(\\sqrt{-3})$ when $d = 3$. Furthermore, our unconditional bounds on perodic points are effectively computable. In the remaining cases, we show that the dynamical uniform boundedness conjecture is implied by the boundedness of Mordell-Weil ranks over $K$ for a specific family of elliptic curves when $d = 3$ and for Jacobians of dynatomic curves when $d = 2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13431",
  "author_total": 1,
  "authors": [
    {
      "name": "Robin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ee5hrety6w4ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13431",
  "fulltext_url": null,
  "id": "ee5hrety6w4ca",
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  "landing_url": "https://arxiv.org/abs/2609.13431",
  "language": null,
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
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      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7213313984",
  "pdf_url": "https://arxiv.org/pdf/2609.13431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ee5hrety6w4ca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.13431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Dynamical uniform boundedness for unicritical polynomials",
  "title_text": "Dynamical uniform boundedness for unicritical polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ee5hrety6w4ca",
  "venue": "arXiv",
  "versions": []
}