Escape from a circle and Riemann hypotheses

Mathematics – Dynamical Systems

Scientific paper

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

Scientific paper

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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