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Noncommutative Geometry and Number Theory

Where Arithmetic meets Geometry and Physics

  • Caterina Consani
  • Matilde Marcolli

Part of the Aspects of Mathematics book series (ASMA)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Anne-Marie Aubert, Paul Baum, Roger Plymen
    Pages 1-34
  3. Florin P. Boca, Alexandru Zaharescu
    Pages 57-77
  4. Alain Connes, Henri Moscovici
    Pages 79-107
  5. Caterina Consani, Matilde Marcolli
    Pages 109-140
  6. Alexander Fel’shtyn, Evgenij Troitsky
    Pages 141-154
  7. Masoud Khalkhali, Bahram Rangipour
    Pages 155-178
  8. Giovanni Landi
    Pages 217-234

About this book

Introduction

In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local Lfactors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Keywords

Archimedean cohomology Farey fractions Formula of Atiyah-Singer Fractional quantum Hall effect Hecke algebra Hopf cyclic cohomology Method of Chabauty Rademacher functions Ramanujan conjecture Reidemeister numbers Schwartz algebra number theory

Editors and affiliations

  • Caterina Consani
    • 1
  • Matilde Marcolli
    • 2
  1. 1.Department of MathematicsThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.Max-Planck-Institut für MathematikBonn

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-8348-0352-8
  • Copyright Information Friedr. Vieweg & Sohn Verlag ∣ GWV Fachverlage GmbH, Wiesbaden 2006
  • Publisher Name Vieweg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-8348-0170-8
  • Online ISBN 978-3-8348-0352-8
  • Series Print ISSN 0179-2156
  • Buy this book on publisher's site
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