L-Functions and Random Matrices

J. Brian Conrey

A chapter in Mathematics Unlimited — 2001 and Beyond, 2001, pp 331-352 from Springer

Abstract: Abstract 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 directions for future investigations.

Date: 2001
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DOI: 10.1007/978-3-642-56478-9_14

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