{
  "abstract": "We classify the arithmetic nature of the Dirichlet eigenvalues of a homogeneous nonlocal one-dimensional $p$-Laplacian problem with power-type nonlinearity $|u|^{q-2}u$. For rational $p,q>1$, either all eigenvalues are algebraic or all are transcendental. Algebraicity holds exactly when the interval length is an algebraic multiple of a distinguished scale determined by a beta value. This scale is transcendental. When $p=q$, the criterion reduces to algebraicity of the interval length divided by $π$,independently of the rational exponent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38471",
  "author_total": 1,
  "authors": [
    {
      "name": "Shingo Takeuchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xxm3rjq5a399.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38471",
  "fulltext_url": null,
  "id": "2xxm3rjq5a399",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38471",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xxm3rjq5a399.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Arithmetic classification of the Dirichlet eigenvalues for a one-dimensional nonlocal $p$-Laplacian problem",
  "title_text": "Arithmetic classification of the Dirichlet eigenvalues for a one-dimensional nonlocal p-Laplacian problem",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2xxm3rjq5a399",
  "venue": "arXiv",
  "versions": []
}