{
  "abstract": "Given any norm $\\|\\cdot\\|_{\\mathbb R^2}$ on $\\mathbb R^2$, we prove that the Lagrange spectrum for $2$-vectors contains a Hall ray. Equivalently, every sufficiently small $ρ\\ge0$ occurs as $\\liminf_{q\\to\\infty}q^{1/2}\\min_{p\\in\\mathbb Z^2}\\|qx-p\\|_{\\mathbb R^2} $ for some $x\\in\\mathbb R^2\\setminus\\mathbb Q^2$. Combined with a recent result of Kleinbock \\cite{Kleinbock}, this implies that the $2$-dimensional Lagrange spectrum is either a ray, mirroring the behavior for Dirichlet spectra, or a ray preceded by a dense part.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23464",
  "author_total": 3,
  "authors": [
    {
      "name": "Yitwah Cheung"
    },
    {
      "name": "Zhijing Wendy Wang"
    },
    {
      "name": "Ruichong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqh8p4q6h7x2c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23464",
  "fulltext_url": null,
  "id": "dqh8p4q6h7x2c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23464",
  "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.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.SP"
    ],
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      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7214030048",
  "pdf_url": "https://arxiv.org/pdf/2609.23464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqh8p4q6h7x2c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Existence of a Hall ray in higher dimensional Lagrange spectra",
  "title_text": "Existence of a Hall ray in higher dimensional Lagrange spectra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dqh8p4q6h7x2c",
  "venue": "arXiv",
  "versions": []
}