{
  "abstract": "We consider Dirichlet $L$-functions $L(s, χ)$ where $χ$ is a quadratic character to modulus $q$. We show that for $χ$ even (resp. odd) $L(σ, χ)\\neq 0$ for all $σ>0$ provided that $q\\leq 10^{9}$ (resp. $q\\leq 10^{10})$. In particular, this result rules out Siegel--Landau zeros for such $L$-functions. Combined, these results improve on previous work by nearly four orders of magnitude. We also list some applications of this work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29018",
  "author_total": 2,
  "authors": [
    {
      "name": "Dave Platt"
    },
    {
      "name": "Tim Trudgian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aq1vzmcbd47xt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29018",
  "fulltext_url": null,
  "id": "aq1vzmcbd47xt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29018",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223228374",
  "pdf_url": "https://arxiv.org/pdf/2610.29018",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aq1vzmcbd47xt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29018",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29018"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Zeros of quadratic Dirichlet $L$-functions",
  "title_text": "Zeros of quadratic Dirichlet L-functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/aq1vzmcbd47xt",
  "venue": "arXiv",
  "versions": []
}