Recent Perspectives in Random Matrix Theory and Number Theory

Francesco Mezzadri, Nina C. Snaith - Collection London Mathematical Society Student Texts

528 pages, parution le 07/12/2005

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Résumé

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.

Self-contained lectures by world-leading experts in the field
The volume is integrated, indexed and cross-referenced
This title covers the most important and recent advances in the subject

L'auteur - Francesco Mezzadri

F. Mezzadri, Editor, University of Bristol

L'auteur - Nina C. Snaith

N. C. Snaith, Edoitor, University of Bristol

Sommaire

Introduction
Prime number theory and the Riemann zeta-function
Notes on pair correlation of zeros and prime numbers
Notes on eigenvalue distributions for the classical compact groups
Compound nucleus resonances, random matrices and quantum chaos
Families of L-functions and 1-level densities
Basic analytic number theory
Applications of mean value theorems to the theory of the Riemann zeta function
L-functions and the characteristic polynomials of random matrices
Mock gaussian behaviour
Some specimens of L-functions
Computational methods and experiments in analytic number theory

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Francesco Mezzadri, Nina C. Snaith
Collection	London Mathematical Society Student Texts
Parution	07/12/2005
Nb. de pages	528
Format	15,5 x 23
Couverture	Broché
Poids	725g
Intérieur	Noir et Blanc
EAN13	9780521620581
ISBN13	978-0-521-62058-1