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nlin.CDAug 30, 2007
24
citations (OpenAlex)
authors
  • Eugene Bogomolny
institutions
  • Centre National de la Recherche Scientifique
  • Laboratoire de Physique Théorique et Modèles Statistiques
  • Université Paris-Sud
arXiv abstractPDF
paper

Riemann zeta function and quantum chaos

arXiv:0708.4223 · doi:10.1143/PTPS.166.19

Abstract

A brief review of recent developments in the theory of the Riemann zeta function inspired by ideas and methods of quantum chaos is given.

Lecture given at International Conference on Quantum Mechanics and Chaos, Osaka, September 2006

References in corpus (2)

  • Quantum and Arithmetical Chaos
  • Spectral statistics and periodic orbits

Cited by in corpus (12)

  • Finite size corrections in random matrix theory and Odlyzko's data set for the Riemann zeros
  • A new proof of the Voronoï summation formula
  • Identifying the Riemann zeros by periodically driving a single qubit
  • Prime numbers and spontaneous neuron activity
  • Analyzing Riemann's hypothesis
  • New approach to periodic orbit theory of spectral correlations
  • Prime zeta function statistics and Riemann zero-difference repulsion
  • The first digit frequencies of primes and Riemann zeta zeros tend to uniformity following a size-dependent generalized Benford's law
  • An experimental study of the monotonicity property of the Riemann zeta function
  • Coulomb Gas Partition Function of a Layered Loop Model
  • On Statistics of the Riemann Zeros Differences
  • Prime numbers: periodicity, chaos, noise
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