Carl Dettmann, Bristol

<H3>Open circular billiards and the Riemann hypothesis</H3>

A comparison of escape rates from one and from two holes in an experimental 
container (e.g.
a laser trap) can be used to obtain information about the dynamics inside 
the container. If this
dynamics is simple enough one can hope to obtain exact formulas. Here we 
obtain exact formulas
for escape from a circular billiard with one and with two holes. The 
corresponding quantities
are expressed as sums over zeroes of the Riemann zeta function. Thus we 
demonstrate a direct
connection between recent experiments and a major unsolved problem in 
mathematics, the Riemann
hypothesis.