{
  "abstract": "Let $K$ be a number field of degree $n$ and discriminant $Δ$. The estimate $|ζ_K(1+it)|\\le C_K\\log{t}$, where $C_K$ is an unspecified constant depending on $K$, is a well--known result in the literature. We obtain an explicit upper bound for $|ζ_K(1+it)|$, depending only on $n$ and $Δ$. We also show how improvements on the bound depend on improvements on estimates of the ideal counting function $I_K$ and the residue of $ζ_K$ at $s=1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32012",
  "author_total": 1,
  "authors": [
    {
      "name": "Giulia Pelizzari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06838mcvf78mq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32012",
  "fulltext_url": null,
  "id": "06838mcvf78mq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32012",
  "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": "W7223687941",
  "pdf_url": "https://arxiv.org/pdf/2610.32012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06838mcvf78mq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32012"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An explicit bound on $|ζ_K(1+it)|$",
  "title_text": "An explicit bound on |ζ_K(1+it)|",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/06838mcvf78mq",
  "venue": "arXiv",
  "versions": []
}