Skip to content
DraconiticResearch
Search Sources API
197,693 studies31 sourcesUpdated 8 min ago
PreprintarXiv licencearXiv

Spectral properties of the Riemann zeta function and their physical applications

  • Kostadin G Gaminchev
Open at sourcePDFDOICite

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 χ2/dof = 1.2; (ii) the role of ζ(3/2) in determining the critical temperature for Bose-Einstein condensation, where we find Tc = 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 −(π2 ℏ c)/(720 a3), which for a=1 nm gives ∼ −4.33×10−4 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.

Related

  1. The Riemann theta function near soliton limit
    Yuji Kodama
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  2. Physical-Prior-Guided Spectral Token Network for Vector Bending Demodulation of Multicore Fiber Bragg Gratings
    lingge gao, xinyu lu, dan zhu +4
    Optics ExpressPeer-reviewedLicence not statedOptics & photonicsCrossref
  3. The MIRI/MRS Library. III. Detector-based optimal spectral extraction and high-contrast imaging applications
    Danny Gasman, Ioannis Argyriou, David R. Law +9
    Astronomy & AstrophysicsPeer-reviewedPublisher termsApplied physics & instrumentationCrossref
  4. Spectral properties of twisted soft waveguides
    Pavel Exner, David Spitzkopf
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsMathematical physicsarXiv
  5. Spectral and transmission properties of multiple correlated quantum dots made simple
    Nahual Sobrino, Stefan Kurth
    arXivPreprintCC BY 4.0Full textCondensed matterarXiv

Cite

BibTeXRIS
BibTeX
@misc{gaminchev2026spectral,
  title = {{Spectral properties of the Riemann zeta function and their physical applications}},
  author = {Kostadin G Gaminchev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04571},
  eprint = {2610.04571},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04571},
}
RIS
TY  - UNPB
TI  - Spectral properties of the Riemann zeta function and their physical applications
AU  - Kostadin G Gaminchev
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04571
UR  - https://arxiv.org/abs/2610.04571
AB  - 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/dof = 1.2; (ii) the role of ζ(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 −(π^2 ℏ c)/(720 a^3), which for a=1 nm gives ∼ −4.33×10^−4 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.
ER  -