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From Number Theory to Physics - Michel Waldschmidt

From Number Theory to Physics

By: Michel Waldschmidt (Editor), Pierre Moussa (Editor), Jean-Marc Luck (Editor), Claude Itzykson (Editor)

Hardcover Published: 9th November 1995
ISBN: 9783540533429
Number Of Pages: 690

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The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti­ cal Physics. The first part is mathematically oriented; it deals mostly with ellip­ tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo­ rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri­ bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com­ munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num­ ber Theory which are the most actively used in their branch.

An Introduction to Zeta Functionsp. 1
Introduction to Compact Riemann Surfaces, Jacobians, and Abelian Varietiesp. 64
Elliptic Curvesp. 212
Introduction to Modular Formsp. 238
Decorated Elliptic Curves: Modular Aspectsp. 292
Galois Theory, Algebraic Number Theory, and Zeta Functionsp. 313
Galois Theory for Coverings and Riemann Surfacesp. 394
Differential Galois Theoryp. 413
p-adic Numbers and Ultrametricityp. 440
Introduction to Lattice Geometryp. 476
A Short Introduction to Quasicrystallographyp. 496
Gap Labelling Theorems for Schrodinger Operatorsp. 538
Circle Maps: Irrationally Windingp. 631
An Introduction to Small Divisors Problemsp. 659
Indexp. 680
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540533429
ISBN-10: 3540533427
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 690
Published: 9th November 1995
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 3.8
Weight (kg): 2.56

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