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Frontiers in Number Theory, Physics and Geometry I: On Random Matrices, Zeta Functions and Dynamical Systems

Pierre Cartier, Bernard Julia, Pierre Moussa, and Pierre Vanhove, editors
Publisher: 
Springer Verlag
Publication Date: 
2006
Number of Pages: 
631
Format: 
Hardcover
Price: 
89.95
ISBN: 
3540231897
Category: 
Proceedings
We do not plan to review this book.

Part I Random Matrices: from Physics to Number Theory

Quantum and Arithmetical Chaos

Eugene Bogomolny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Notes on L-functions and Random Matrix Theory

J. Brian Conrey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Energy Level Statistics, Lattice Point Problems, and Almost

Modular Functions

Jens Marklof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Arithmetic Quantum Chaos of Maass Waveforms

H. Then . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Large N Expansion for Normal and Complex Matrix

Ensembles

P. Wiegmann, A. Zabrodin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Symmetries Arising from Free Probability Theory

Dan Voiculescu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Universality and Randomness for the Graphs and Metric

Spaces

A. M. Vershik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Part II Zeta Functions

From Physics to Number Theory via Noncommutative

Geometry

Alain Connes, Matilde Marcolli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

XII Contents

More Zeta Functions for the Riemann Zeros

Andr´e Voros. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

Hilbert Spaces of Entire Functions and Dirichlet L-Functions

Jeffrey C. Lagarias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

Dynamical Zeta Functions and Closed Orbits for Geodesic

and Hyperbolic Flows

Mark Pollicott . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

Part III Dynamical Systems: interval exchange, flat surfaces, and

small divisors

Continued Fraction Algorithms for Interval Exchange Maps:

an Introduction

Jean-Christophe Yoccoz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

Flat Surfaces

Anton Zorich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

Brjuno Numbers and Dynamical Systems

Guido Gentile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

Some Properties of Real and Complex Brjuno Functions

Stefano Marmi, Pierre Moussa, Jean-Christophe Yoccoz. . . . . . . . . . . . . . . 603

Part IV Appendices

List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

Dummy View - NOT TO BE DELETED