Quantum chaos, Random Matrix theory, and the Riemann ζ-function

Paul Bourgade, Jonathan P. Keating

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

14 Citations (Scopus)


We review some connections between quantum chaos and the theory of the Riemann zeta function and the primes. Specifically, we give an overview of the similarities between the semiclassical trace formula that connects quantum energy levels and classical periodic orbits in chaotic systems and an analogous formula that connects the Riemann zeros and the primes. We also review the role played by Random Matrix Theory in both quantum chaos and the theory of the zeta function. The parallels we review are conjectural and still far from being understood, but the ideas have led to substantial progress in both areas.

Original languageEnglish
Title of host publicationChaos
Subtitle of host publicationPoincaré Seminar 2010
PublisherBirkhäuser Basel
Number of pages44
ISBN (Print)9783034806961
Publication statusPublished - 1 Jan 2013
Event14th Poincare Seminar 2010: Chaos - Paris, United Kingdom
Duration: 5 Jun 20105 Jun 2010

Publication series

NameProgress in Mathematical Physics


Conference14th Poincare Seminar 2010: Chaos
Country/TerritoryUnited Kingdom


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