Pierre Cartier / Bernard Julia / Pierre Moussa / Pierre Vanhove (eds.)

Frontiers in Number Theory, Physics, and Geometry I

On Random Matrices, Zeta Functions, and Dynamical Systems
Herausgeber: Cartier, Pierre; Julia, Bernard; Moussa, Pierre, Herausgegeben:Cartier, Pierre E.; Julia, Bernard; Moussa, Pierre; Vanhove, Pierre

• Gebundenes Buch

Produktbeschreibung

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent.

More than ten years after a first meeting in 1989 between number theorists and physicists at the Centre de Physique des Houches, a second 2-week event focused on the broader interface of number theory, geometry, and physics.

This book is the result of that exciting meeting, and collects, in 2 volumes, extended versions of the lecture courses, followed by shorter texts on special topics, of eminent mathematicians and physicists.

The present volume has three parts: Random matrices, Zeta functions, Dynamical systems.

The companion volume is subtitled: On Conformal Field Theories, Discrete Groups and Renormalization and will be published in 2006 (Springer, 3-540-30307-3).

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Produktdetails

• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-23189-9
• 2006
• Seitenzahl: 652
• Erscheinungstermin: 16. Dezember 2005
• Englisch
• Abmessung: 241mm x 160mm x 45mm
• Gewicht: 1036g
• ISBN-13: 9783540231899
• ISBN-10: 3540231897
• Artikelnr.: 14761453

Autorenporträt

Pierre Emile Cartier, IHES, Bures-sur-Yvette, France / Bernard Julia, ENS-CRNS/LTP, Paris, France / Pierre Moussa, CEA/Saclay, Gif-sur -Yvette, France / Pierre Vanhove, CEA/Saclay, Gif-sur-Yvette, France

Inhaltsangabe

Random Matrices: from Physics to Number Theory.- Quantum and Arithmetical Chaos.- Notes on L-functions and Random Matrix Theory.- Energy Level Statistics, Lattice Point Problems, and Almost Modular Functions.- Arithmetic Quantum Chaos of Maass Waveforms.- Large N Expansion for Normal and Complex Matrix Ensembles.- Symmetries Arising from Free Probability Theory.- Universality and Randomness for the Graphs and Metric Spaces.- Zeta Functions.- From Physics to Number Theory Via Noncommutative Geometry.- More Zeta Functions for the Riemann Zeros.- Hilbert Spaces of Entire Functions and Dirichlet L-Functions.- Dynamical Zeta Functions and Closed Orbits for Geodesic and Hyperbolic Flows.- Dynamical Systems: Interval Exchange, Flat Surfaces, and Small Divisors.- Continued Fraction Algorithms for Interval Exchange Maps: an Introduction.- Flat Surfaces.- Brjuno Numbers and Dynamical Systems.- Some Properties of Real and Complex Brjuno Functions.