{
  "abstract": "We study the distribution of the number of coprime lattice points in randomly translated disks. We prove that its spatial variance is asymptotic to $σ^2r\\log r$ and establish a central limit theorem under the corresponding normalization, where $σ^2$ is an explicit positive constant. By truncating the numerators of rational frequencies in lowest terms, the proof reduces higher-moment estimates to counting squarefree denominators in zero-sum relations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14224",
  "author_total": 1,
  "authors": [
    {
      "name": "Xin Hang Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5e19yeb7csynx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14224",
  "fulltext_url": null,
  "id": "5e19yeb7csynx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14224",
  "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.NT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7213307542",
  "pdf_url": "https://arxiv.org/pdf/2609.14224",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5e19yeb7csynx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14224",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14224"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Central Limit Theorem for Coprime Pair Counts in Randomly Translated Disks",
  "title_text": "A Central Limit Theorem for Coprime Pair Counts in Randomly Translated Disks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5e19yeb7csynx",
  "venue": "arXiv",
  "versions": []
}