{
  "abstract": "Let $M_d(X)$ denote the average number of rational preperiodic points among degree-$d$ polynomials over $\\mathbb{Q}$ with vanishing $z^{d-1}$ coefficient, constant term $1$, and height at most $X$. We prove that, for every integer $d\\ge2$, $M_d(X) \\sim γ_d X^{-1}$ for an explicit constant $γ_d>0$. For $d\\ge4$, the error term is $O_{d,\\varepsilon}(X^{-2+\\varepsilon})$ for every $\\varepsilon>0$; for $d=3$ the error term is $O(X^{-3/2})$; and for $d=2$ the error term is $O(X^{-3/2}\\log X)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29383",
  "author_total": 1,
  "authors": [
    {
      "name": "Jungin Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6v9spmbzj03fd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29383",
  "fulltext_url": null,
  "id": "6v9spmbzj03fd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29383",
  "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.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204908197",
  "pdf_url": "https://arxiv.org/pdf/2608.29383",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6v9spmbzj03fd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2608.29383",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29383"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The average number of rational preperiodic points of polynomials over $\\mathbb{Q}$",
  "title_text": "The average number of rational preperiodic points of polynomials over ℚ",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/6v9spmbzj03fd",
  "venue": "arXiv",
  "versions": []
}