{
  "abstract": "Denote by $\\Phi_m(X,Y)\\in\\Z[X,Y]$, $m\\geqslant 1$ the sequence of binary cyclotomic forms, so that $\\Phi_m(T,1)\\in\\Z[T]$, $m\\geqslant 1$ is the sequence of cyclotomic polynomials. We prove that, for $m\\geqslant 3$, the fundamental domain \\[ \\calO_m:= \\{ (x,y)\\in\\R^2\\; \\mid \\; \\Phi_m(x,y)\\leqslant 1\\} \\] of $\\Phi_m$ is a convex subset of $\\R^2$ if and only if $m$ is equal to $p$, $2p$ or $2^k$ with $p$ an odd prime and $k\\geqslant 2$. Finally we investigate the convexity of the fundamental domains attached to some products of binary forms $\\Phi_m$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Polynesian Journal of Mathematics, 2026, 4 (7), pp.1-14",
  "arxiv": "2610.37735",
  "author_total": 2,
  "authors": [
    {
      "name": "Étienne Fouvry"
    },
    {
      "name": "Michel Waldschmidt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7h2fe9ha8r79z.bib",
  "cited_by": 0,
  "doi": "10.69763/polyjmath.4.7",
  "fulltext_url": null,
  "id": "7h2fe9ha8r79z",
  "issns": [
    "3075-3422",
    "3075-3422"
  ],
  "landing_url": "https://hal.science/hal-05837700v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-nt"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214683028",
  "pdf_url": "https://hal.science/hal-05837700/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7h2fe9ha8r79z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05837700",
      "source": "hal",
      "url": "https://hal.science/hal-05837700v1"
    },
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37735"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the convexity of the fundamental domain of binary cyclotomic forms",
  "title_text": "On the convexity of the fundamental domain of binary cyclotomic forms",
  "type": "peer-reviewed",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7h2fe9ha8r79z",
  "venue": "Polynesian Journal of Mathematics",
  "versions": []
}