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Escape from a circle and Riemann hypotheses

Leonid A. Bunimovich·Carl P. Dettmann
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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.

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Leonid A. Bunimovich, Carl P. Dettmann. 2006-03-15. Escape from a circle and Riemann hypotheses. https://arxiv.org/abs/math/0603373

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