{
  "abstract": "We establish sharp bounds for rational points near compact smooth nondegenerate curves in $\\mathbb R^n$, for every $n\\geq4$. For a nondegenerate curve $\\mathcal C$ in $\\mathbb R^n$, let \\[ \\mathcal R_{\\mathcal C}(δ,Q) :=\\#\\left\\{(\\mathbf p,q)\\in\\mathbb Z^n\\times\\mathbb N: 1\\leq q\\leq Q,\\ \\operatorname{dist}(\\mathbf p/q,\\mathcal C)\\leqδ/q\\right\\}.\\] We prove that \\[\\mathcal R_{\\mathcal C}(δ,Q) \\lesssim_{\\varepsilon,\\mathcal C} δ^{n-1}Q^2+Q^\\varepsilon \\left(Q+\\sum_{k=1}^{n-1} δ^{k^2/(k+1)}Q^{(2k+1)/(k+1)}\\right).\\] A key new ingredient is a wave packet method developed by Gan--Maldague--Oh.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03231",
  "author_total": 3,
  "authors": [
    {
      "name": "Shengwen Gan"
    },
    {
      "name": "Shaoming Guo"
    },
    {
      "name": "Changkeun Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4q3maw2f2c54h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03231",
  "fulltext_url": null,
  "id": "4q3maw2f2c54h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03231",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7220375649",
  "pdf_url": "https://arxiv.org/pdf/2610.03231",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4q3maw2f2c54h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03231",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03231"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp rational points counting near nondegenerate curves in $\\mathbb{R}^n$",
  "title_text": "Sharp rational points counting near nondegenerate curves in ℝ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/4q3maw2f2c54h",
  "venue": "arXiv",
  "versions": []
}