{
  "abstract": "The complex polynomial Bohnenblust--Hille inequality bounds the coefficient $\\ell_{2m/(m+1)}$ norm of a complex $m$-homogeneous polynomial by its supremum norm, with a constant independent of the number of variables. For each fixed integer $N\\ge3$, we characterize the choices of $N$ degree-$m$ monomials for which the inequality holds with optimal constant $1$ for every polynomial supported on them, provided $m$ exceeds an explicit threshold depending only on $N$. This holds precisely when their exponent vectors contain no nontrivial three-term arithmetic progression; equality for a nonzero polynomial then holds only for monomials. We also prove that, in the same degree range, every polynomial with at most $N$ nonzero coefficients that violates the constant-one inequality has a unique coefficient of maximal modulus, whose exponent is the center of such a progression in its support. Exact contractivity also follows from a comparability condition on the two largest coefficients, with a degree threshold that necessarily depends on the number of nonzero monomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36887",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel M. Pellegrino"
    },
    {
      "name": "Eduardo V. Teixeira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2k03rqvat3bh0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36887",
  "fulltext_url": null,
  "id": "2k03rqvat3bh0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36887",
  "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": "W7224101390",
  "pdf_url": "https://arxiv.org/pdf/2610.36887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2k03rqvat3bh0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Rigidity of Exact Contractivity in the Complex Polynomial Bohnenblust--Hille Inequality",
  "title_text": "Rigidity of Exact Contractivity in the Complex Polynomial Bohnenblust--Hille Inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/2k03rqvat3bh0",
  "venue": "arXiv",
  "versions": []
}