{
  "abstract": "We determine the dimension-free threshold for the comparison between the Bombieri--Weyl norm and the supremum norm of complex homogeneous polynomials on $\\ell_p^n$. For $m$-homogeneous polynomials, the critical scale is $p=2m$: below this threshold no dimension-free comparison is possible, while at $p=2m$ we obtain $\\|P\\|_{\\mathrm{BW}}\\le (1+C/m)\\|P\\|_{2m}$. Moreover, there exist absolute constants $A>0$ and $m_0\\in\\mathbb N$ such that, for every $m\\ge m_0$ and $p\\ge 2m+A$, $\\|P\\|_{\\mathrm{BW}}\\le\\|P\\|_p$, with optimal constant one. Equality holds precisely for coordinate pure powers. We also obtain a quantitative stability statement for near-extremizers. The proof is based on a decomposition by multiplicity patterns, contractive orbit projections, Hardy--Littlewood estimates for reduced multilinear forms, and Wiener-type slice estimates. Finally, we show that the corresponding contractive phenomenon fails over the real scalar field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13753",
  "author_total": 4,
  "authors": [
    {
      "name": "Daniel Nunez-Alarcon"
    },
    {
      "name": "Daniel M. Pellegrino"
    },
    {
      "name": "Anselmo Raposo Jr."
    },
    {
      "name": "Eduardo V. Teixeira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4f1czkmr21nn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13753",
  "fulltext_url": null,
  "id": "4f1czkmr21nn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13753",
  "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": "W7203621393",
  "pdf_url": "https://arxiv.org/pdf/2608.13753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4f1czkmr21nn9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2608.13753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13753"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Bombieri--Weyl Contractivity and Rigidity for Homogeneous Polynomials",
  "title_text": "Bombieri--Weyl Contractivity and Rigidity for Homogeneous Polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/4f1czkmr21nn9",
  "venue": "arXiv",
  "versions": []
}