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Number Theory and Physics

Proceedings of the Winter School, Les Houches, France, March 7–16, 1989

  • Jean-Marc Luck
  • Pierre Moussa
  • Michel Waldschmidt

Part of the Springer Proceedings in Physics book series (SPPHY, volume 47)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Conformally Invariant Field Theories, Integrability, Quantum Groups

  3. Quasicrystals and Related Geometrical Structures

  4. Spectral Problems, Automata and Substitutions

  5. Dynamical and Stochastic Systems

    1. Front Matter
      Pages 203-203
    2. F. M. Dekking
      Pages 204-208
    3. J. S. Geronimo
      Pages 209-215
    4. S. Golin, A. Knauf, S. Marmi
      Pages 216-222
    5. D. Verstegen
      Pages 235-242
  6. Further Arithmetical Problems, and Their Relationship to Physics

    1. Front Matter
      Pages 243-243
    2. P. Cassou-Noguès
      Pages 244-252
    3. M. L. Mehta
      Pages 253-259
    4. C. J. Smyth
      Pages 260-263
    5. B. Julia
      Pages 276-293
    6. J. P. Keating
      Pages 302-310
  7. Back Matter
    Pages 311-314

About these proceedings

Introduction

7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu­ tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with "small denominators", as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string theory of fundamental interactions, completely integrable models, and conformally invariant two-dimensional field theories, seems to involve modular forms and p­ adic numbers in a remarkable way.

Keywords

Riemann zeta function algebraic number theory arithmetic crystal dynamical systems number theory quasicrystal theoretical physics zeta function

Editors and affiliations

  • Jean-Marc Luck
    • 1
  • Pierre Moussa
    • 1
  • Michel Waldschmidt
    • 2
  1. 1.Service de Physique ThéoriqueC.E.N SaclayGif-sur-Yvette CedexFrance
  2. 2.Institut Henri-Poincaré, Problèmes DiophantiensUniversité de Paris 6Paris Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-75405-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-75407-4
  • Online ISBN 978-3-642-75405-0
  • Series Print ISSN 0930-8989
  • Series Online ISSN 1867-4941
  • Buy this book on publisher's site
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