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Fonction zeta et matrices aléatoires
Book chapter   Open access

Fonction zeta et matrices aléatoires

Emmanuel Royer
Physics and number theory, pp.165--224
IRMA Lectures in Mathematics and Theoretical Physics Vol. 10
2006

Abstract

Since Euler and Riemann, various links have been established between the behaviour of prime numbers and the analytical properties of the Riemann ζ function. The zeroes of ζ have a great importance that justifies their fine study. Since seventies, a rich tool has appeared for the study of zeroes : the statistical spectral properties of the unitary matrices that are a model for ζ. The aim of this survey is to explain the link between unitary matrices and ζ, and its extension to the L-functions..
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