Overview

Various developments in physics have involved many questions related to number theory, in an increasingly direct way. This trend is especially visible in two broad families of problems, namely, field theories, and dynamical systems and chaos. The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on ""Number Theory and Physics"" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagogical viewpoint.

Full Product Details

Author:   Michel Waldschmidt ,  P. Cartier ,  Pierre Moussa ,  J.-B. Bost
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1992
Dimensions:   Width: 15.50cm , Height: 3.50cm , Length: 23.50cm
Weight:   1.068kg
ISBN:  

9783642080975

ISBN 10:   3642080979
Pages:   690
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

1. An Introduction to Zeta Functions.- 2. Introduction to Compact Riemann Surfaces, Jacobians, and Abelian Varieties.- 3. Elliptic Curves.- 4. Introduction to Modular Forms.- 5. Decorated Elliptic Curves: Modular Aspects.- 6. Galois Theory, Algebraic Number Theory, and Zeta Functions.- 7. Galois Theory for Coverings and Riemann Surfaces.- 8. Differential Galois Theory.- 9. p-adic Numbers and Ultrametricity.- 10. Introduction to Lattice Geometry.- 11. A Short Introduction to Quasicrystallography.- 12. Gap Labelling Theorems for Schroedinger Operators.- 13. Circle Maps: Irrationally Winding.- 14. An Introduction to Small Divisors Problems.

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