{
  "abstract": "We give a general classification theorem for cyclotomic algebraic integers with all complex absolute values bounded by a fixed constant $c$, modeled on the theorem of Cassels which treats the case $c = \\sqrt{5}$ up to finitely many exceptions. As a corollary, we establish that the range of the function taking a cyclotomic integer to its maximum complex absolute value is a well-ordered (but not closed) subset of the real numbers. We also formulate analogous statements for algebraic numbers in the maximal cyclotomic extension of a fixed number field. The proofs combine a result of Loxton, which bounds the number of roots of unity in the shortest additive representation of a cyclotomic integer in terms of the maximum complex absolute value, with an equidistribution theorem of Bilu et al. for Galois orbits of torsion points on algebraic tori.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05853",
  "author_total": 4,
  "authors": [
    {
      "name": "Jitendra Bajpai"
    },
    {
      "name": "Srijan Das"
    },
    {
      "name": "Kiran S. Kedlaya"
    },
    {
      "name": "Jorge Mello"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ae39gn6j34x4f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05853",
  "fulltext_url": null,
  "id": "ae39gn6j34x4f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05853",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212066923",
  "pdf_url": "https://arxiv.org/pdf/2609.05853",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ae39gn6j34x4f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.05853",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05853"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the classification of small cyclotomic integers",
  "title_text": "On the classification of small cyclotomic integers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ae39gn6j34x4f",
  "venue": "arXiv",
  "versions": []
}