{
  "abstract": "The Jensen--Pólya criterion expresses the generalized Riemann hypothesis (GRH) for Dedekind zeta-functions as a real-rootedness condition on their Jensen polynomials. Previous asymptotic results require large shifts, while computations establish real-rootedness in the Riemann case through a finite range of degrees. Here we study the unshifted family as the degree tends to infinity. For every number field $K$, we prove unconditionally that $J_{K,d}(X)$ is nonzero and has at least $d-C_K\\sqrt{d\\log d}$ distinct negative real zeros for all sufficiently large $d$, where $C_K>0$ depends only on $K$. Therefore, the proportion of real zeros tends to one with error $O_K(\\sqrt{\\log d/d})$. The main theorems have been autoformalized in Lean~4 by AxiomProver.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38870",
  "author_total": 1,
  "authors": [
    {
      "name": "Ken Ono"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31kwt3t7pkacf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38870",
  "fulltext_url": null,
  "id": "31kwt3t7pkacf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38870",
  "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.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38870",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31kwt3t7pkacf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38870",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38870"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An asymptotic Jensen-Polya criterion for GRH",
  "title_text": "An asymptotic Jensen-Polya criterion for GRH",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/31kwt3t7pkacf",
  "venue": "arXiv",
  "versions": []
}