2006/03/15 by Leonid A. Bunimovich, Leonid Bunimovich, Bunimovich, Leonid A. +2
Mathematics · Physics and Astronomy · #37A45 #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #History and Theory of Mathematics #Mathematical Physics (math-ph) #Number Theory (math.NT) #math-ph #math.DS #math.MP #math.NT #msc:37A45 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0603373
24 pages, proofs and extensions of results in nlin.SI/0408009
arxiv created 2006/03/15 · openalex publication_date 2006/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.