{
  "abstract": "We prove strict Pólya inequalities for every positive Neumann eigenvalue of every Euclidean annulus. The proof preserves the exact Weyl area term through a radial action identity and combines variational bounds with uniform Bessel-phase and angular-sum estimates. Explicit polynomial positivity arguments and angular-layer comparisons cover the remaining finite spectral ranges. We also obtain a positive counting surplus uniform in the radius ratio, an explicit subtraction of order $\\sqrt{k}/(R^2-r^2)$ for all $k\\ge1604$, and a positive square-root correction over the entire spectrum with a universal, non-explicit coefficient. The square-root order is sharp, and the first positive pair and the low-energy count admit optimal constants expressed by the first positive zero of $J_1'$. Neumann inequalities for annular products and congruent annular sectors follow by established transfer principles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05146",
  "author_total": 2,
  "authors": [
    {
      "name": "Guowei Dai"
    },
    {
      "name": "Yingxin Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7n6f1ed1p5ck.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05146",
  "fulltext_url": null,
  "id": "a7n6f1ed1p5ck",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05146",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7220698829",
  "pdf_url": "https://arxiv.org/pdf/2610.05146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7n6f1ed1p5ck.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.05146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05146"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Pólya's conjecture for Neumann eigenvalues of annuli",
  "title_text": "Pólya's conjecture for Neumann eigenvalues of annuli",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/a7n6f1ed1p5ck",
  "venue": "arXiv",
  "versions": []
}