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Aspects of Mathematics

Noncommutative Geometry and Number Theory

Where Arithmetic meets Geometry and Physics

Editors: Consani, Caterina, Marcolli, Matilde (Eds.)

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  • Aktuelles aus der mathematischen Forschung

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About this Textbook

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.

About the authors

Prof. Dr. Caterina Consani, Department of Mathematics, The Johns Hopkins University, Baltimore, USA
Prof. Dr. Matilde Marcolli, Max-Planck Institute for Mathematics, Bonn, Germany

Table of contents (17 chapters)

Table of contents (17 chapters)
  • The Hecke algebra of a reductive p-adic group: a geometric conjecture

    Pages 1-34

    Aubert, Anne-Marie (et al.)

  • Hilbert modular forms and the Ramanujan conjecture

    Pages 35-56

    Blasius, Don

  • Farey fractions and two-dimensional tori

    Pages 57-77

    Boca, Florin P. (et al.)

  • Transgressions of the Godbillon-Vey Class and Rademacher functions

    Pages 79-107

    Connes, Alain (et al.)

  • Archimedean cohomology revisited

    Pages 109-140

    Consani, Caterina (et al.)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-8348-0352-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-3-8348-2673-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Noncommutative Geometry and Number Theory
Book Subtitle
Where Arithmetic meets Geometry and Physics
Editors
  • Caterina Consani
  • Matilde Marcolli
Series Title
Aspects of Mathematics
Series Volume
37
Copyright
2006
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden
eBook ISBN
978-3-8348-0352-8
DOI
10.1007/978-3-8348-0352-8
Softcover ISBN
978-3-8348-2673-2
Series ISSN
0179-2156
Edition Number
1
Number of Pages
VIII, 372
Topics

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