{
  "abstract": "We establish o-minimal definability results and develop point-counting machinery applicable to the zeros of a Bessel function of fixed non-negative real parameter. We also give an Ax-Schanuel theorem for Bessel functions of fixed (complex) parameters and exponential functions. We combine these to prove a sparsity result (weak Manin-Mumford) for points on an algebraic variety whose coordinates are zeros of a Bessel function of fixed (non-negative real) parameter. We apply this result to improve density results on spectral sets for the unit ball motivated by Fuglede's conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28477",
  "author_total": 4,
  "authors": [
    {
      "name": "Gal Binyamini"
    },
    {
      "name": "Avner Kiro"
    },
    {
      "name": "Gady Kozma"
    },
    {
      "name": "Jonathan Pila"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8dhrxs2arfnt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28477",
  "fulltext_url": null,
  "id": "c8dhrxs2arfnt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28477",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223122378",
  "pdf_url": "https://arxiv.org/pdf/2610.28477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8dhrxs2arfnt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28477"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Counting Bessel zeros and applications",
  "title_text": "Counting Bessel zeros and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/c8dhrxs2arfnt",
  "venue": "arXiv",
  "versions": []
}