L-functions and random matrices

Details L-functions and random matrices L-functions and random matrices

2000-05-31

arxiv.org/abs/math/0005300v1

Mathematics

Number Theory

Abstract added in migration (from introduction).

Scientific paper

In 1972 H. L. Montgomery announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices. Since then a number of startling developments have occurred making this connection more profound. In particular, random matrix theory has been found to be an extremely useful predictive tool in the theory of L-functions. In this article we will try to explain these recent developments and indicate some diretions for future investigations.

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