2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110207We 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.24 pages, proofs and extensions of results in nlin.SI/0408009Dynamical SystemsMathematical PhysicsNumber TheoryExactly Solvable and Integrable Systems37A45text