Escape from a circle and Riemann hypotheses
动力系统
2007-05-23 v1 数学物理
math.MP
数论
可精确求解与可积系统
摘要
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.
关键词
引用
@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}
}
备注
24 pages, proofs and extensions of results in nlin.SI/0408009