{
  "abstract": "Let $R = \\mathbb{Z}[\\sqrt{14}]$, let $π= 4 + \\sqrt{14}$, and let $\\mathfrak{p} = (2,\\sqrt{14}) = πR$ be the prime ideal above $2$. Cavallar and Lemmermeyer studied the multiplicative weighted norms $ϕ_{t}(x) = |N(x)|(t/2)^{v_π(x)}$ and asked for which weights $t$ they are Euclidean functions on $R$. We show that the set of these weights, the Euclidean window of $\\mathfrak{p}$, is $(\\sqrt{5},T]$, where $T$ is the algebraic number \\[ T = \\sqrt{\\frac{8}{104051\\sqrt{2} - 55617\\sqrt{7}}} = 2.2468286690\\ldots = \\sqrt{5} + 0.0107606915\\ldots. \\] Thus the window is nonempty but not open. We also obtain the integer-valued completely multiplicative Euclidean function $2^{v_π(x)}|N(x)|^{6}$ on $R$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24309",
  "author_total": 1,
  "authors": [
    {
      "name": "David A. Cardon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09s9pppec1wds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24309",
  "fulltext_url": null,
  "id": "09s9pppec1wds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24309",
  "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": "W7223010271",
  "pdf_url": "https://arxiv.org/pdf/2610.24309",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09s9pppec1wds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24309",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24309"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The exact Euclidean window of $\\mathbb{Z}[\\sqrt{14}]$",
  "title_text": "The exact Euclidean window of ℤ[√(14)]",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/09s9pppec1wds",
  "venue": "arXiv",
  "versions": []
}