Escape from a circle and Riemann hypotheses

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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.
24 pages, proofs and extensions of results in nlin.SI/0408009

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Dynamical Systems, Mathematical Physics, Number Theory, Exactly Solvable and Integrable Systems, 37A45

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http://salesiana.dossiersoluciones.com/handle/123456789/110207

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603373
 http://arxiv.org/abs/math/0603373

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arXiv