{
  "abstract": "In their previous work devoted to the distribution of rational points near Brownian motion, the authors conjectured the existence of an \\emph{oscillation principle} governing the asymptotic behavior of the number of rational points with bounded denomi\\-nators near the graph of a monofractal curve. In this note, a weaker form of this conjecture is shown to hold for a broad class of deterministic fractal curves. These include the classical Takagi and Weierstrass nowhere differentiable functions, and indeed a prevalent (i.e.~\"large\") class of functions among those which are Hölder continuous with a given exponent of regularity. This constitutes the first instance of deterministic fractal curves for which a precise count of the rational points under consideration is established.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16377",
  "author_total": 3,
  "authors": [
    {
      "name": "Faustin Adiceam"
    },
    {
      "name": "Volodymyr Pavlenkov"
    },
    {
      "name": "Evgeniy Zorin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ds0da3j12hmc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16377",
  "fulltext_url": null,
  "id": "1ds0da3j12hmc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16377",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7213439340",
  "pdf_url": "https://arxiv.org/pdf/2609.16377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ds0da3j12hmc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16377"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Rational Points near Monofractal Curves and the Strong Oscillation Principle",
  "title_text": "Rational Points near Monofractal Curves and the Strong Oscillation Principle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/1ds0da3j12hmc",
  "venue": "arXiv",
  "versions": []
}