{
  "abstract": "Recently, a uniform $\\frac{7}{8}$ zero-free half-plane for finite-order Hecke $L$-functions over $\\mathbb Q(\\sqrt{-3})$ and its transfer to Dirichlet $L$-functions was given by OpenAI in [Ope26a]. In its proof, there are several parameters $b=\\frac{1}{8}, \\ell=\\frac{1}{6}$, and $κ$. In this paper, via varying $b$, $\\ell$, and $κ$, following the same strategy, we slightly improve the bound $\\frac{7}{8}=0.875$ to \\[ B_{\\mathrm{new}}=\\frac{18ξ_{\\mathrm{new}}+7}{18ξ_{\\mathrm{new}}+9} =0.874957019420098946\\ldots, \\] where $ξ_{\\mathrm{new}}$ is the unique root in $(0.38858,0.38859)$ of $1188ξ^3-2160ξ^2+171ξ+190=0$. Explicitly, with $\\arccos\\in[0,π]$, \\[ ξ_{\\mathrm{new}}=\\frac{20}{33}+\\frac{\\sqrt{1391}}{33} \\cos\\!\\left(\\frac13\\arccos\\frac{28470}{1391^{3/2}} -\\frac{2π}{3}\\right). \\] The limiting parameters are \\[ \\begin{gathered} b_{\\mathrm{new}}=\\frac{8(3ξ_{\\mathrm{new}}-1)(12ξ_{\\mathrm{new}}^2-40ξ_{\\mathrm{new}}+15)} {9(2ξ_{\\mathrm{new}}+1)(24ξ_{\\mathrm{new}}^2-20ξ_{\\mathrm{new}}+5)}, \\ell_{\\mathrm{new}}=\\frac{5-6ξ_{\\mathrm{new}}}{9+18ξ_{\\mathrm{new}}},\\qquad κ_{\\mathrm{new}}=\\frac{18ξ_{\\mathrm{new}}+5}{18ξ_{\\mathrm{new}}+9} =2B_{\\mathrm{new}}-1. \\end{gathered} \\] We also prove its optimality within the explicitly specified exponent comparison system. This result has been formalized by Lean [Liu26].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12234",
  "author_total": 1,
  "authors": [
    {
      "name": "Baiying Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dwavz7rsmjp1s.bib",
  "cited_by": 5,
  "doi": "10.48550/arxiv.2610.12234",
  "fulltext_url": null,
  "id": "dwavz7rsmjp1s",
  "issns": [
    "2331-8422"
  ],
  "landing_url": "https://arxiv.org/abs/2610.12234",
  "language": "en",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221107878",
  "pdf_url": "https://arxiv.org/pdf/2610.12234",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "Cornell University",
  "ris": "https://research.draconitic.com/paper/dwavz7rsmjp1s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.12234",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12234"
    },
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W7221107878",
      "source": "openalex",
      "url": "https://arxiv.org/abs/2610.12234"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Improved zero-free half-planes for the quasi-Riemann hypothesis",
  "title_text": "Improved zero-free half-planes for the quasi-Riemann hypothesis",
  "type": "preprint",
  "updated_at": "2026-11-04T13:21:00Z",
  "url": "https://research.draconitic.com/paper/dwavz7rsmjp1s",
  "venue": "arXiv",
  "versions": []
}