{
  "abstract": "For functions $f : [0,1] \\to [0,1]$ in quasianalytic Denjoy-Carleman classes $\\mathcal C_M$, we establish explicit bounds for the number of intersection points of the graph $Γ(f)$ with algebraic curves of degree at most $d$. The bounds are given in terms of the Bang degree determined by the weight sequence $M$, the degree $d$, and the norming constant of $Γ(f)$ with respect to the space of real bivariate polynomials of degree at most $d$. We give instances, where the bounds are at most polynomial in $d$ and, consequently, the graph $Γ(f)$ contains few rational points: the number of rational points of height at most $H$ is bounded by a polynomial in $\\log H$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21725",
  "author_total": 1,
  "authors": [
    {
      "name": "Armin Rainer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/377t7wfa7f22a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21725",
  "fulltext_url": null,
  "id": "377t7wfa7f22a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21725",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222477512",
  "pdf_url": "https://arxiv.org/pdf/2610.21725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/377t7wfa7f22a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21725"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Bézout bounds and rational points on quasianalytic graphs",
  "title_text": "Bézout bounds and rational points on quasianalytic graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/377t7wfa7f22a",
  "venue": "arXiv",
  "versions": []
}