Escape from a circle and Riemann hypotheses
Dynamical Systems
2007-05-23 v1 Mathematical Physics
math.MP
Number Theory
Exactly Solvable and Integrable Systems
Abstract
We consider open circular billiards with one and with two holes. The exact formulas for escape are obtained which involve the Riemann zeta function and Dirichlet L-functions. It is shown that the problem of finding the exact asymptotics in the small hole limit for escape in some of these billiards is equivalent to the Riemann hypothesis.
Keywords
Cite
@article{arxiv.math/0603373,
title = {Escape from a circle and Riemann hypotheses},
author = {Leonid A. Bunimovich and Carl P. Dettmann},
journal= {arXiv preprint arXiv:math/0603373},
year = {2007}
}
Comments
24 pages, proofs and extensions of results in nlin.SI/0408009