{
  "abstract": "Let $K$ be a number field of degree $n_K$, and let $h(K)$ denote the smallest absolute value of the imaginary part of a non-trivial zero of its Dedekind zeta function. In 1979, Hoffstein proved the unconditional bound $h(K)\\leq 0.87+o(1)$ as $n_K\\to\\infty$. In a 1990 survey article, Odlyzko stated without proof that a different kernel in Weil's explicit formula could produce $h(K)\\leq 0.54+o(1)$. No further improvement on Hoffstein's $0.87$ threshold accompanied by a published proof has since appeared. We choose a linear kernel and first show that Hoffstein's original parameters already yield the improved constant $0.825$. We then generalise his linear kernel method using Stechkin's trick and prove the unconditional bound $h(K)\\leq 0.6+o(1)$ as $n_K\\to\\infty$, giving the best proved asymptotic bound to date.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16010",
  "author_total": 2,
  "authors": [
    {
      "name": "Timothy S. Trudgian"
    },
    {
      "name": "Sebastian Zuniga-Alterman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1d1rp9cqymw5q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16010",
  "fulltext_url": null,
  "id": "1d1rp9cqymw5q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16010",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221749479",
  "pdf_url": "https://arxiv.org/pdf/2610.16010",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1d1rp9cqymw5q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16010",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16010"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Low Lying Zeros of Dedekind Zeta Functions",
  "title_text": "Low Lying Zeros of Dedekind Zeta Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1d1rp9cqymw5q",
  "venue": "arXiv",
  "versions": []
}