TY - GEN
T1 - Quantum chaos, Random Matrix theory, and the Riemann ζ-function
AU - Bourgade, Paul
AU - Keating, Jonathan P.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84896787687&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84896787687&partnerID=8YFLogxK
U2 - 10.1007/978-3-0348-0697-8_4
DO - 10.1007/978-3-0348-0697-8_4
M3 - Conference contribution
AN - SCOPUS:84896787687
SN - 9783034806961
T3 - Progress in Mathematical Physics
SP - 125
EP - 168
BT - Chaos
PB - Birkhauser Boston
T2 - 14th Poincare Seminar 2010: Chaos
Y2 - 5 June 2010 through 5 June 2010
ER -