Recent Perspectives in Random Matrix Theory and Number Theory

ISBN-13: 9780521620581 / Angielski / Miękka / 2005 / 532 str.

F. Mezzadri; N. C. Snaith; N. J. Hitchin

Opis

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.

Spis treści

1. Introduction; 2. Prime number theory and the Riemann zeta-function; 3. Notes on pair correlation of zeros and prime numbers; 4. Notes on eigenvalue distributions for the classical compact groups; 5. Compound nucleus resonances, random matrices and quantum chaos; 6. Families of L-functions and 1-level densities; 7. Basic analytic number theory; 8. Applications of mean value theorems to the theory of the Riemann zeta function; 9. L-functions and the characteristic polynomials of random matrices; 10. Mock gaussian behaviour; 11. Some specimens of L-functions; 12. Computational methods and experiments in analytic number theory.