Recent Perspectives in Random Matrix Theory and Number Theory

doi:10.1017/CBO9780511550492

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Recent Perspectives in Random Matrix Theory and Number Theory

Recent Perspectives in Random Matrix Theory and Number Theory

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Cited by 32
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Edited by F. Mezzadri, University of Bristol, N. C. Snaith, University of Bristol

Publisher:: Cambridge University Press
Online publication date:: January 2010
Print publication year:: 2005
Online ISBN:: 9780511550492
DOI:: https://doi.org/10.1017/CBO9780511550492

Subjects:: Mathematics (general), Mathematics, Number Theory, Probability Theory and Stochastic Processes, Statistics and Probability
Series:: London Mathematical Society Lecture Note Series (322)

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In recent years the application of random matrix techniques to analytic number theory has been responsible for major advances in this area of mathematics. As a consequence it has created a new and rapidly developing area of research. The aim of this book is to provide the necessary grounding both in relevant aspects of number theory and techniques of random matrix theory, as well as to inform the reader of what progress has been made when these two apparently disparate subjects meet. This volume of proceedings is addressed to graduate students and other researchers in both pure mathematics and theoretical physics. The contributing authors, who are among the world leading experts in this area, have taken care to write self-contained lectures on subjects chosen to produce a coherent volume.

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Recent Perspectives in Random Matrix Theory and Number Theory

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Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp vii-x

Prime number theory and the Riemann zeta-function
pp 1-30

Introduction to the random matrix theory: Gaussian Unitary Ensemble and beyond
pp 31-78

Notes on pair correlation of zeros and prime numbers
pp 79-110

Notes on eigenvalue distributions for the classical compact groups
pp 111-146

Compound nucleus resonances, random matrices, quantum chaos
pp 147-184

Basic analytic number theory
pp 185-200

Applications of mean value theorems to the theory of the Riemann zeta function
pp 201-224

Families of L-functions and 1-level densities
pp 225-250

L-functions and the characteristic polynomials of random matrices
pp 251-278

Spacing distributions in random matrix ensembles
pp 279-308

Toeplitz determinants, Fisher-Hartwig symbols, and random matrices
pp 309-336

Mock-Gaussian behaviour
pp 337-356

Some specimens of L-functions
pp 357-424

Computational methods and experiments in analytic number theory
pp 425-510

Index
pp 511-518

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Recent Perspectives in Random Matrix Theory and Number Theory

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