×

Random Matrix Theory and the distribution of zeros of \({L}\)-functions. (Répartition des zéros des fonctions \(L\) et matrices aléatoires.) (French) Zbl 1075.11056

Bourbaki seminar. Volume 2000/2001. Exposés 880-893. Paris: Société Mathématique de France (ISBN 2-85629-130-9/pbk). Astérisque 282, 211-248, Exp. No. 887 (2002).
The random matrix theory has shed new light on problems concerning the distribution of the zeros of \(L\)-functions and their mean values. The author gives a comprehensive survey of the active research going on in this field. A salient feature of modern analytic number theory, emphasized also by the author, is the close interplay between the classical theory (Riemann’s zeta-function and Dirichlet’s \(L\)-functions) and the theory of automorphic functions. There is an extensive bibliography with about 50 references.
For the entire collection see [Zbl 1007.00024].

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11M41 Other Dirichlet series and zeta functions
11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
15B52 Random matrices (algebraic aspects)
PDFBibTeX XMLCite
Full Text: Numdam