{
  "abstract": "A Hardy space approach to the Nyman-Beurling and Báez-Duarte criterion for the Riemann Hypothesis (RH) was introduced in [7]. It states that the RH holds if and only if the span of a particular sequence of functions $(h_k)_{k\\geq2}$, denoted $\\mathcal{N}$, is dense in the Hardy space $H^2$. In this note we construct a bounded operator $T$ on $H^{2}$ such that if the closure of $\\mathcal{N}$ is $T$-invariant, then either the RH holds or there exists an infinite progression of $ζ$-zeros. In particular, this yields an operator-theoretic criterion for the Riemann hypothesis as an invariant subspace question.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03568",
  "author_total": 2,
  "authors": [
    {
      "name": "Juan Manzur"
    },
    {
      "name": "Waleed Noor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zd8xrnp9wfzw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03568",
  "fulltext_url": null,
  "id": "7zd8xrnp9wfzw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03568",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7220363181",
  "pdf_url": "https://arxiv.org/pdf/2610.03568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zd8xrnp9wfzw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03568"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Hardy-space operator acting on $ζ$-zeros",
  "title_text": "A Hardy-space operator acting on ζ-zeros",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/7zd8xrnp9wfzw",
  "venue": "arXiv",
  "versions": []
}