Recent Perspectives in Random Matrix Theory and Number Theory -

Recent Perspectives in Random Matrix Theory and Number Theory

F. Mezzadri, N. C. Snaith (Herausgeber)

Buch | Softcover
532 Seiten
2005
Cambridge University Press (Verlag)
978-0-521-62058-1 (ISBN)
89,95 inkl. MwSt
In recent years the application of random matrix techniques to analytic number theory has been responsible for major advances in this area of mathematics. The aim of this book is to provide the necessary grounding as well as to inform the reader of recent progress.
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.

Francesco Mezzadri is a Lecturer in Applied Mathematics at the University of Bristol. Nina Snaith is a Lecturer in Applied Mathematics at the University of Bristol.

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.

Erscheint lt. Verlag 21.6.2005
Reihe/Serie London Mathematical Society Lecture Note Series
Verlagsort Cambridge
Sprache englisch
Maße 153 x 228 mm
Gewicht 727 g
Themenwelt Mathematik / Informatik Mathematik
ISBN-10 0-521-62058-9 / 0521620589
ISBN-13 978-0-521-62058-1 / 9780521620581
Zustand Neuware
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