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

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.

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.

Zusammenfassung

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.

Produktdetails

• Mitarbeit: Pierre E. Cartier (Herausgeber), Bernar Julia (Herausgeber), Bernard Julia (Herausgeber), Pierre Moussa (Herausgeber), Pierre Moussa et al (Herausgeber), Pierre Vanhove (Herausgeber)
• Verlag: Springer, Berlin
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 13.10.2010
• EAN: 9783642062193
• ISBN: 978-3-642-06219-3
• Seiten: 624
• Abmessung: 156 mm x 36 mm x 238 mm
• Gewicht: 972 g
• Illustration: XII, 624 p.
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Arithmetik, Algebra; C, Mathematische Physik, Algebraische Geometrie, Mathematics and Statistics, Algebraic Geometry, Theoretical, Mathematical and Computational Physics, Number Theory, Mathematical physics, zeta functions