{
  "abstract": "For complex \\(m\\)-homogeneous polynomials, let \\(D_m\\) denote the optimal dimension-free constant in the polynomial Bohnenblust--Hille inequality. We prove that, for every \\(B>1/2\\), there exists \\(K_B>0\\) such that \\[ D_m\\le K_B m^B,\\qquad m\\ge1. \\] More precisely, we obtain the square-root-scale estimate \\[ D_m\\le \\sqrt m\\,\\exp\\!\\bigl(C\\sqrt{\\log m}\\,\\log\\log m\\bigr). \\] The proof combines coefficient-preserving degree reduction with a weighted bootstrap, separating balanced and dominant degree profiles. We also determine the critical linear-dimensional asymptotics: \\[ D_{m,n_m}\\longrightarrow 2 \\qquad\\text{whenever}\\qquad \\frac{n_m}{m}\\longrightarrow1, \\] and consequently \\(\\liminf_{m\\to\\infty}D_m\\ge2\\). Further applications give two-sided bounds for homogeneous Sidon constants and a quantitative logarithmic remainder in the multidimensional Bohr-radius asymptotic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.16584",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel M. Pellegrino"
    },
    {
      "name": "Eduardo V. Teixeira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jnqmzk5we0bd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.16584",
  "fulltext_url": null,
  "id": "5jnqmzk5we0bd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.16584",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7203694766",
  "pdf_url": "https://arxiv.org/pdf/2608.16584",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jnqmzk5we0bd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2608.16584",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.16584"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Polynomial growth of complex polynomial Bohnenblust--Hille constants",
  "title_text": "Polynomial growth of complex polynomial Bohnenblust--Hille constants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5jnqmzk5we0bd",
  "venue": "arXiv",
  "versions": []
}