From Number Theory to Physics (eBook, PDF)

Redaktion: Waldschmidt, Michel; Itzykson, Claude; Luck, Jean-Marc; Moussa, Pierre

• Format: PDF

Produktbeschreibung

Recent 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 system 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 on original pedagogical viewpoint.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 690
• Erscheinungstermin: 9. März 2013
• Englisch
• ISBN-13: 9783662028384
• Artikelnr.: 53105049

Inhaltsangabe

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 Schrödinger Operators.- 13. Circle Maps: Irrationally Winding.- 14. An Introduction to Small Divisors Problems.