{
  "abstract": "We give two explicit reformulations of a Balazard--Saias--Yor type criterion for the Riemann hypothesis. First, Jensen's formula is applied to $u(s)=(s-1)ζ(s)$ after mapping the unit disk onto $Re s<1/2$. For the normalization whose center corresponds to $s=-1/2$, the images $z_n=(4n-1)/(4n+3)$ of the trivial zeros yield a telescoping Jensen product. This isolates, at finite radius, the complete divergent contribution of the trivial zeros; the remaining defect is a nonnegative integrated count of mapped nontrivial zeros off the critical line. A one-parameter version gives a gamma-quotient product and an explicit finite part. Second, after passing through the established boundary identity, we combine two Poisson weights to obtain an absolutely convergent logarithmic integral of the Riemann $Ξ$-function. From the random variable $Z=|Ξ(T)/Ξ(0)|^2$ we define its law $μ$ and the size-biased law $ν(\\,\\mathrm d z)=zμ(\\,\\mathrm d z)/M$. The data-processing inequality is lossless for this statistic, and the Riemann hypothesis is equivalent to saturation of an explicit upper bound for $D_{\\rm KL}(μ\\|ν)$. We also record the associated Donsker--Varadhan and moment forms and express the target constant through Riemann's positive Fourier kernel. The analytic boundary criterion and Jensen--Hardy mechanism used here are known. The purpose of the paper is an explicit finite-radius treatment of the trivial zeros and an information-theoretic reformulation, not a new proof of the Riemann hypothesis or an independent boundary-integral criterion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10584",
  "author_total": 1,
  "authors": [
    {
      "name": "Henning Wunderlich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brgstqfwq5933.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10584",
  "fulltext_url": null,
  "id": "brgstqfwq5933",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10584",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221162449",
  "pdf_url": "https://arxiv.org/pdf/2610.10584",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brgstqfwq5933.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10584",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10584"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-radius Jensen and relative-entropy formulations of the Balazard--Saias--Yor criterion",
  "title_text": "Finite-radius Jensen and relative-entropy formulations of the Balazard--Saias--Yor criterion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/brgstqfwq5933",
  "venue": "arXiv",
  "versions": []
}