{
  "abstract": "Let $(a_n)_{n\\geq0}$ be a sequence of complex numbers, and define \\[ b_n=\\sum_{k=0}^n \\binom{n}{k} a_k, \\qquad c_n=\\sum_{k=0}^n \\binom{n}{k}(-1)^{n-k}a_k. \\] Let $β>1$, put $α=\\sqrt{β^2-1}$, and suppose that $b_n,c_n=O(β^n)$. Mashreghi and Ransford proved that \\[ \\limsup_{n\\to\\infty}\\frac{|a_n|}{α^n} \\leq κ\\left(\\limsup_{n\\to\\infty}\\frac{|b_n|}{β^n}\\right)^{\\!1/2}\\! \\left(\\limsup_{n\\to\\infty}\\frac{|c_n|}{β^n}\\right)^{\\!1/2} \\] with a universal constant satisfying $2/\\sqrt{3} \\leq κ\\leq2$. We prove that the optimal constant is indeed $κ=2/\\sqrt{3}$. The proof, which uses exponential generating functions, Phragmén-Lindelöf estimates, and Cauchy's formula, is compared to the classical one of Mashreghi and Ransford.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08852",
  "author_total": 1,
  "authors": [
    {
      "name": "Ludovick Bouthat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qdvzbvcph2wy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08852",
  "fulltext_url": null,
  "id": "7qdvzbvcph2wy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08852",
  "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.CO"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7211988348",
  "pdf_url": "https://arxiv.org/pdf/2609.08852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qdvzbvcph2wy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08852"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The sharp constant in the Mashreghi-Ransford inequality",
  "title_text": "The sharp constant in the Mashreghi-Ransford inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/7qdvzbvcph2wy",
  "venue": "arXiv",
  "versions": []
}