{
  "abstract": "Fix an integer $K\\ge2$, and let $C_K^n =\\{(e^{\\frac{2πij}{K}})_{j=0}^{K-1}\\}^n$ be the product of cyclic groups of order $K$. For a Fourier character $χ_α$, let $s(α)$ be the number of active coordinates. We give a self-contained proposed proof that the dimension-free Bohnenblust--Hille constants governed by interaction order grow polynomially: if $p_d=2d/(d+1)$ and \\[ γ_2=\\frac12, \\qquad γ_K=\\frac{K\\log(K-1)}{4(K-2)}\\quad(K\\ge3), \\] then the $\\ell^{p_d}$ norm of Fourier coefficients $\\{\\hat f(α)\\}$ is bounded by $L^\\infty$ norm of $f$ multiplied by $C(K) d^{4γ_K+5}$. The constant $C(K)$ is actually at most of the order $K^{5/2}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07758",
  "author_total": 2,
  "authors": [
    {
      "name": "Joseph Slote"
    },
    {
      "name": "Alexander Volberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8r60r94b0bqvf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07758",
  "fulltext_url": null,
  "id": "8r60r94b0bqvf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07758",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212087388",
  "pdf_url": "https://arxiv.org/pdf/2609.07758",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8r60r94b0bqvf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.07758",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07758"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Polynomial Bohnenblust--Hille bounds for product of cyclic groups",
  "title_text": "Polynomial Bohnenblust--Hille bounds for product of cyclic groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/8r60r94b0bqvf",
  "venue": "arXiv",
  "versions": []
}