{
  "abstract": "An equivalent version of the Báez-Duarte criterion \\cite{baez} for the Riemann Hypothesis (RH) by Bagchi states that the RH holds true if and only if the function $E(s) = 1/s$ belongs to the closed linear span of $G_k(s) = (k^{-s} - k^{-1})ζ(s)/s,\\, k \\geq 2$ in the Hardy space \\( H^2(\\mathbb{C}_{1/2}) \\), where $\\mathbb{C}_α$ denotes the half-plane $\\mathrm{Re}(s)>α$. We first show that if $E$ belongs to the closure of span$(G_k)_{k\\geq 2}$ in \\( H^2(\\mathbb{C}_α) \\) for $α>1/2$, then $ζ$ is zero-free in $\\mathbb{C}_α$. We then use this as the basis for a numerical analysis of the sequence \\[ s_n = \\left\\| \\sum_{k=2}^{n} μ(k) G_k - E \\right\\|^2_α, \\] for $1/2\\leq α\\leq 1$, where $\\left\\|.\\right\\|_α$ is the norm in $H^2(\\mathbb{C}_α)$ and $μ$ the Möbius function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16097",
  "author_total": 3,
  "authors": [
    {
      "name": "Juan Manzur"
    },
    {
      "name": "Waleed Noor"
    },
    {
      "name": "Gustavo Quintero"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4fejds0eyyh9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16097",
  "fulltext_url": null,
  "id": "d4fejds0eyyh9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.16097",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7164923588",
  "pdf_url": "https://arxiv.org/pdf/2606.16097",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4fejds0eyyh9.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2606.16097",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16097"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Hardy space approximation supporting zero-free half-planes for the $ζ$-function",
  "title_text": "A Hardy space approximation supporting zero-free half-planes for the ζ-function",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/d4fejds0eyyh9",
  "venue": "arXiv",
  "versions": []
}