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9780521620581

Recent Perspectives in Random Matrix Theory and Number Theory

by
  • ISBN13:

    9780521620581

  • ISBN10:

    0521620589

  • Format: Paperback
  • Copyright: 2005-07-11
  • Publisher: Cambridge University Press

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Summary

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 the progress made when the two apparently disparate subjects meet. This volume of proceedings is addressed to graduate students and other researchers in both pure mathematics and theoretical physics.

Table of Contents

Introduction vii
F. Mezzadri and N.C. Snaith
Prime number theory and the Riemann zeta-function 1(30)
D.R. Heath-Brown
Introduction to the random matrix theory: Gaussian Unitary Ensemble and beyond 31(48)
Yan V. Fyodorov
Notes on pair correlation of zeros and prime numbers 79(32)
D.A. Goldston
Notes on eigenvalue distributions for the classical compact groups 111(36)
Brian Conrey
Compound nucleus resonances, random matrices, quantum chaos 147(38)
Oriol Bohigas
Basic analytic number theory 185(16)
David W. Farmer
Applications of mean value theorems to the theory of the Riemann zeta function 201(24)
S.M. Gonek
Families of L-functions and 1-level densities 225(26)
Brian Conrey
L-functions and the characteristic polynomials of random matrices 251(28)
J.P. Keating
Spacing distributions in random matrix ensembles 279(30)
Peter J. Forrester
Toeplitz determinants, Fisher-Hartwig symbols, and random matrices 309(28)
Estelle L. Basor
Mock-Gaussian behaviour 337(20)
C.P. Hughes
Some specimens of L-functions 357(68)
Philippe Michel
Computational methods and experiments in analytic number theory 425
Michael Rubinstein
Index

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