{
  "abstract": "This work studies the Riemann $ζ$ numerically with emphasis on its physical manifestations. Three areas are examined: (i) the spectral statistics of the non-trivial zeros, which we compare with the Gaussian Unitary Ensemble predictions, obtaining $χ^2/\\text{dof} = 1.2$; (ii) the role of $ζ(\\frac{3}{2})$ in determining the critical temperature for Bose-Einstein condensation, where we find $T_c = 0.13$ K for an ideal gas; and (iii) the application of $ζ$-function regularisation to the Casimir effect, yielding the standard Casimir energy density $-\\frac{π^2 \\hbar c}{720 a^3}$, which for $a=1\\,\\mathrm{nm}$ gives $\\sim -4.33\\times10^{-4}\\,\\mathrm{J\\,m^{-2}}$. The numerical results are consistent with the Montgomery-Odlyzko conjecture and with spectral approaches motivated by the Hilbert-Pólya conjecture, within the statistical limitations of the analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04571",
  "author_total": 1,
  "authors": [
    {
      "name": "Kostadin G Gaminchev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7wd78byhadehr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04571",
  "fulltext_url": null,
  "id": "7wd78byhadehr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04571",
  "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",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7220659008",
  "pdf_url": "https://arxiv.org/pdf/2610.04571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7wd78byhadehr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.04571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04571"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Spectral properties of the Riemann zeta function and their physical applications",
  "title_text": "Spectral properties of the Riemann zeta function and their physical applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/7wd78byhadehr",
  "venue": "arXiv",
  "versions": []
}