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

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Pierre E. Cartier Bernard Julia

Frontiers in Number Theory, Physics, and Geometry I

On Random Matrices, Zeta Functions, and Dynamical Systems

Pierre E. Cartier, Bernard Julia, Pierre Moussa , Pierre Vanhove

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English

Springer Verlag
01 June 2006

Mathematics & Sciences; Number theory; Algebraic geometry; Physics

This book presents pedagogical contributions on selected topics relating Number Theory, Theoretical Physics and Geometry. The parts are composed of long self-contained pedagogical lectures followed by shorter contributions on specific subjects organized by theme. Most courses and short contributions go up to the recent developments in the fields; some of them follow their author's original viewpoints. There are contributions on Random Matrix Theory, Quantum Chaos, Non-commutative Geometry, Zeta functions, and Dynamical Systems. The chapters of this book are extended versions of lectures given at a meeting entitled Number Theory, Physics and Geometry, held at Les Houches in March 2003, which gathered mathematicians and physicists.

Edited by: Pierre E. Cartier, Bernard Julia, Pierre Moussa, Pierre Vanhove, Pierre Vanhove (CEA/Saclay, Gif-sur-Yvette, France)
Imprint: Springer Verlag
Country of Publication: Germany
Dimensions: Height: 235mm, Width: 155mm, Spine: 36mm
Weight: 1.252kg
ISBN: 9783540231899
ISBN 10: 3540231897
Pages: 652
Publication Date: 01 June 2006
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.