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.
Author(s): Michel Waldschmidt, Pierre Moussa, Jean-Marc Luck, Claude Itzykson, P. Cartier, J.-B. Bost, H. Cohen, D. Zagier, R. Gergondey, H.M. Stark, E. Reyssat, F. Beukers, G. Christol, M. Senechal, A. Katz, J. Bellissard, P. Cvitanovic, J.-C. Yoccoz
Edition: Corrected
Publisher: Springer
Year: 2001
Language: English
Pages: 704
Tags: Физика;Матметоды и моделирование в физике;
Contents......Page all_1263_to_00701.cpc0010.djvu
Preface......Page all_1263_to_00701.cpc0002.djvu
1. An Introduction to Zeta Functions......Page all_1263_to_00701.cpc0012.djvu
2. Introduction to Compact Riemann Surfaces, Jacobians, and Abelian Varieties......Page all_1263_to_00701.cpc0075.djvu
3. Elliptic Curves......Page all_1263_to_00701.cpc0223.djvu
4. Introduction to Modular Forms......Page all_1263_to_00701.cpc0249.djvu
5. Decorated Elliptic Curves: Modular Aspects......Page all_1263_to_00701.cpc0303.djvu
6. Galois Theory, Algebraic Number Theory, and Zeta Functions......Page all_1263_to_00701.cpc0324.djvu
7. Galois Theory for Coverings and Riemann Surfaces......Page all_1263_to_00701.cpc0405.djvu
8. Differential Galois Theory......Page all_1263_to_00701.cpc0424.djvu
9. p-adic Numbers and Ultrametricity......Page all_1263_to_00701.cpc0451.djvu
10. Introduction to Lattice Geometry......Page all_1263_to_00701.cpc0487.djvu
11. A Short Introduction to Quasicrystallography......Page all_1263_to_00701.cpc0507.djvu
12. Gap Labelling Theorems for Schrodinger Operators......Page all_1263_to_00701.cpc0549.djvu
13. Circle Maps: Irrationally Winding......Page all_1263_to_00701.cpc0642.djvu
14. An Introduction to Small Divisors Problems......Page all_1263_to_00701.cpc0670.djvu
Index......Page all_1263_to_00701.cpc0691.djvu
