{
  "abstract": "For a quasi-projective arithmetic surface $\\mathcal U/\\mathbb Z$ and a compact subset $E\\subset \\mathcal U(\\mathbb C)$ under mild regularity assumptions, we study algebraic integral points on $\\mathcal U$ whose Galois orbits lie in $E$. We characterize the collections of local probability measures that arise simultaneously as the local limit distributions of Galois orbits of such points. Our result also works for measures prescribed at a subset of places. This generalizes the results of Smith and Orloski--Sardari on $\\mathcal{U}=\\mathbb{A}^1$ concerning the archimedean place. As a consequence, we prove an integral version of Szachniewicz's theorem on curves, which states that every \\emph{integral} GVF functional can be approximated by a sequence of algebraic integral points in the GVF topology. We also give several applications: we prove that the essential minimum of height functions on curves can be attained by algebraic integral points; we connect integer Chebyshev constants with the essential minima of certain height functions on $\\mathbb{A}^1$ and prove a conjecture of Montgomery; we also answer affirmatively a question of Levenberg--Londhe by showing that the smallest limit of averaged trace of totally positive algebraic integers can be attained by a sequence of totally positive algebraic units.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39505",
  "author_total": 2,
  "authors": [
    {
      "name": "Binggang Qu"
    },
    {
      "name": "Chengyuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/de0mmdj4j54ba.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39505",
  "fulltext_url": null,
  "id": "de0mmdj4j54ba",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39505",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7215032646",
  "pdf_url": "https://arxiv.org/pdf/2609.39505",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/de0mmdj4j54ba.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39505",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39505"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Limit distribution of algebraic integral points on curves",
  "title_text": "Limit distribution of algebraic integral points on curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/de0mmdj4j54ba",
  "venue": "arXiv",
  "versions": []
}