{
  "abstract": "Let $Q\\geq 1$ be large, and $δ\\in(0,1)$ be small. Denote by $\\mathcal C \\subset \\mathbb R^3$ a sufficiently smooth curve with non-vanishing curvature and torsion. How many rational points $\\mathbf{a}/q$ of height $q\\in[1, Q]$ are $δ/q$-near $\\mathcal C$? This manuscript provides an essentially optimal answer, thereby addressing a problem stated by Beresnevich and Kleinbock, for space curves. We show that the folklore conjectures are incorrect for certain manifolds with codimension $\\ge 2$, including the moment curve $(t,t^2,t^3)$. The reason is a {hitherto} hidden `major arc' type obstruction. We also establish matching upper bounds, up to endpoints. Our argument combines purely Fourier analytical techniques with the planar counting results by Vaughan and Velani.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09009",
  "author_total": 4,
  "authors": [
    {
      "name": "Mingfeng Chen"
    },
    {
      "name": "Andreas Seeger"
    },
    {
      "name": "Rajula Srivastava"
    },
    {
      "name": "Niclas Technau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tm52r3k1ckhy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09009",
  "fulltext_url": null,
  "id": "6tm52r3k1ckhy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09009",
  "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.CA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7202165373",
  "pdf_url": "https://arxiv.org/pdf/2608.09009",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tm52r3k1ckhy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.09009",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09009"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Bounds for Rational Points Near Space Curves",
  "title_text": "Sharp Bounds for Rational Points Near Space Curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/6tm52r3k1ckhy",
  "venue": "arXiv",
  "versions": []
}