Frontiers in Number Theory, Physics, and Geometry I

On Random Matrices, Zeta Functions, and Dynamical Systems
1. Auflage 2005. Corr. 2. printing. Softcover version of original hardcover Auflage 2006
ISBN: 978-3-642-06219-3
Verlag: Springer

Buch, Englisch, 624 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 972 g

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 10 years after a first meeting between number theorists and physicists at the Centre de Physique des Houches, a second two-week event focused on the broader interface of number theory, geometry, and physics. This book collects the material presented at this meeting.

Zielgruppe

Research

Autoren/Hrsg.

Cartier, Pierre E.

Julia, Bernard

Moussa, Pierre

Vanhove, Pierre

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik

Inhaltsverzeichnis

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.