{
  "abstract": "The Riemann hypothesis is equivalent to $F(x)$ belonging to the Laguerre--Pólya class. Brändén [J. Reine Angew. Math., 2011] proved that if an entire function in the Laguerre--Pólya class has nonnegative Taylor coefficients, then its coefficient sequence is infinitely log-concave. Consequently, the Riemann hypothesis implies the infinite log-concavity of $(λ_n)_{n\\ge0}$. In this paper, we prove that the sequence $(λ_n)_{n\\ge0}$ is strictly infinitely log-concave. This resolves a conjecture of Zhu [Math. Z., 2023]. The proof combines explicit complex-analytic estimates for the iterated logarithmic ratios, rigorous interval arithmetic for a finite range of indices, and a global closure argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04972",
  "author_total": 2,
  "authors": [
    {
      "name": "Yanxin Liu"
    },
    {
      "name": "Jianxi Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ehp12eag2cxvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04972",
  "fulltext_url": null,
  "id": "ehp12eag2cxvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04972",
  "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.CO"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7220737181",
  "pdf_url": "https://arxiv.org/pdf/2610.04972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ehp12eag2cxvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04972"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Infinite log-concavity of the Taylor coefficients of the Riemann xi-function",
  "title_text": "Infinite log-concavity of the Taylor coefficients of the Riemann xi-function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ehp12eag2cxvs",
  "venue": "arXiv",
  "versions": []
}