{
  "abstract": "The goal of this paper is to prove an upper bound for the $L^4$ norm of a trigonometric polynomial whose spectrum is a nontrivial strictly monotone polynomial with integer coefficients of degree three and higher, via its $L^2$ norm. Our condition on the coefficients of the trigonometric polynomial in question is that they form a complex sequence whose modulus is decreasing. Second, we obtain a similar result in the case where the spectrum is formed by perfect squares, under a more strict condition on the coefficients. Our results strengthen and complement those by S. Bochkarev and A. Córdoba. We also give an answer to a conjecture of Eceizabarrena and Da Rocha and determine the sharp order of growth of the $L^4$ norm of the trigonometric polynomial in this conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19132",
  "author_total": 1,
  "authors": [
    {
      "name": "Ioann Vasilyev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90f8c6s47vr6n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19132",
  "fulltext_url": null,
  "id": "90f8c6s47vr6n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19132",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7203865176",
  "pdf_url": "https://arxiv.org/pdf/2608.19132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90f8c6s47vr6n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.19132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Norm bounds on Fourier series with polynomial spectra and constrained coefficients",
  "title_text": "Norm bounds on Fourier series with polynomial spectra and constrained coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/90f8c6s47vr6n",
  "venue": "arXiv",
  "versions": []
}