{
  "abstract": "Let $f$ be an analytic function in the unit disc whose modulus is bounded by $1$. We present a new proof of Bohr's theorem, which asserts that its majorant function $Mf(r)$ is bounded by $1$ for $0\\leq r \\leq 1/3$ and that $1/3$ is optimal. The argument also yields a sharp upper bound for $Mf(r)$ in terms of $\\lvert f(0) \\rvert$, complementing a result due to Bombieri.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26850",
  "author_total": 1,
  "authors": [
    {
      "name": "Ole Fredrik Brevig"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3x9ptmn4t9p5z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26850",
  "fulltext_url": null,
  "id": "3x9ptmn4t9p5z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26850",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7214230976",
  "pdf_url": "https://arxiv.org/pdf/2609.26850",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3x9ptmn4t9p5z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26850",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26850"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A bootstrap proof of Bohr's theorem",
  "title_text": "A bootstrap proof of Bohr's theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/3x9ptmn4t9p5z",
  "venue": "arXiv",
  "versions": []
}