L-Functions and Random Matrices

By J. Brian Conrey. 2000

79 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f068a0b82651f832854373e131d5d296b992d858

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In Algebra and Number Theory

Neil O'Connell

In Discrete Mathematics and Combinatorics

In Mathematical Physics

Citations in the corpus

PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE (2003, methodology): “Much of this work is carefully reviewed in Conrey [22], Berry and Keating [12] and Katz-Sarnak [59].”