Mathematical Sciences: Classical Analysis, Number Theory and Quantum Chaos

Hejhal DMS-9424368 Hejhal will use high-performance computers to investigate three topics: analytic number theory, automorphic forms and the Selberg trace formalism, and quantum chaos. In number theory, the PI will be seeking a better understanding of the zeros of various kinds of zeta functions. He will be focusing on the asymptotic spacing pattern in the zeros and seeking to reconcile this with certain statistical ensembles arising in random matrix theory. This work has important application to fundamental and long-standing questions in number theory. It also leads to new uses of supercomputing in the more theoretical areas of mathematical analysis, both as an experimental tool and one which can give sharp probability estimates in situations where precise information is too difficult to extract from the functions definitions.