TY - GEN

T1 - Quantum chaos, Random Matrix theory, and the Riemann ζ-function

AU - Bourgade, Paul

AU - Keating, Jonathan P.

PY - 2013/1/1

Y1 - 2013/1/1

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

U2 - 10.1007/978-3-0348-0697-8_4

DO - 10.1007/978-3-0348-0697-8_4

M3 - Conference Contribution (Conference Proceeding)

AN - SCOPUS:84896787687

SN - 9783034806961

VL - 66

T3 - Progress in Mathematical Physics

SP - 125

EP - 168

BT - Chaos

PB - Birkhäuser Basel

T2 - 14th Poincare Seminar 2010: Chaos

Y2 - 5 June 2010 through 5 June 2010

ER -