On random matrices, zeta functions, and dynamical systems
著者
書誌事項
On random matrices, zeta functions, and dynamical systems
（Frontiers in number theory, physics, and geometry, 1）
Springer, c2006
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注記
Includes bibliographical references and index
Pagination of corrected second printing 2006: xii, 638 p
"The first printing of this book had to be withdrawn and replaced by this corrected 2nd printing, when unanticipated numbering errors were discovered in several articles"--p. viii of Corr. 2nd printing
内容説明・目次
内容説明
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.
目次
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.
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