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Recent perspectives in random matrix theory and number theory. Proceedings of a school that was part of the programme ‘Random matrix approaches in number theory’, Cambridge, UK, January 26–July 16, 2004. (English) Zbl 1065.11002

London Mathematical Society Lecture Note Series 322. Cambridge: Cambridge University Press (ISBN 0-521-62058-9/pbk). ix, 518 p. (2005).

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Publisher’s description: 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.
The articles of this volume will be reviewed individually.
Indexed articles:
Heath-Brown, D. R., Prime number theory and the Riemann zeta-function, 1-30 [Zbl 1204.11144]
Fyodorov, Yan V., Introduction to the random matrix theory: Gaussian unitary ensemble and beyond, 31-78 [Zbl 1204.11151]
Goldston, D. A., Notes on pair correlation of zeros and prime numbers, 79-110 [Zbl 1168.11320]
Conrey, Brian, Notes on eigenvalue distributions for the classical compact groups, 111-145 [Zbl 1204.11142]
Bohigas, Oriol, Compound nucleus resonances, random matrices, quantum chaos, 147-183 [Zbl 1204.81193]
Farmer, David W., Basic analytic number theory, 185-200 [Zbl 1204.11137]
Gonek, S. M., Applications of mean value theorems to the theory of the Riemann zeta function, 201-223 [Zbl 1204.11138]
Conrey, Brian, Families of \(L\)-functions and 1-level densities, 225-249 [Zbl 1204.11149]
Keating, J. P., \(L\)-functions and the characteristic polynomials of random matrices, 251-277 [Zbl 1204.11152]
Forrester, Peter J., Spacing distributions in random matrix ensembles, 279-307 [Zbl 1204.82024]
Basor, Estelle L., Toeplitz determinants, Fisher-Hartwig symbols, and random matrices, 309-336 [Zbl 1168.82314]
Hughes, C. P., Mock-Gaussian behaviour, 337-355 [Zbl 1168.11322]
Michel, Philippe, Some specimens of \(L\)-functions, 357-424 [Zbl 1204.11174]
Rubinstein, Michael, Computational methods and experiments in analytic number theory, 425-506 [Zbl 1168.11329]

MSC:

11-06 Proceedings, conferences, collections, etc. pertaining to number theory
00B25 Proceedings of conferences of miscellaneous specific interest
11M50 Relations with random matrices
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
15B52 Random matrices (algebraic aspects)
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
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