Vieweg Aspects of Mathematics 2006; 372 pp; hardcover Volume: 37 ISBN10: 3834801704 ISBN13: 9783834801708 List Price: US$113 Member Price: US$101.70 Order Code: VWAM/37
 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 uptodate 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 \(L\)factors 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. A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan. Readership Graduate students and research mathematicians interested in geometry and topology. Table of Contents  A.M. Aubert, P. Baum, and R. Plymen  The Hecke algebra of a reductive \(p\)adic group: a view from noncommutative geometry
 D. Blasius  Hilbert modular forms and the Ramanujan conjecture
 F. P. Boca and A. Zaharescu  Farey fractions and twodimensional tori
 A. Connes and H. Moscovici  Transgression of the GodbillonVey class and Rademacher functions
 C. Consani and M. Marcolli  Archimedean cohomology revisited
 A. Fel'shtyn and E. Troitsky  A twisted Burnside theorem for countable groups and Reidemeister numbers
 M. Khalkhali and B. Rangipour  Introduction to Hopf cyclic cohomology
 M. Kim  The nonabelian (or nonlinear) method of Chabauty
 D. Kreimer  The residues of quantum field theorynumbers we should know
 M. Laca and M. van Frankenhuijsen  Phase transitions with spontaneous symmetry breaking on Hecke \(C^\ast\)algebras from number fields
 G. Landi  On harmonic maps in noncommutative geometry
 M. Marcolli and V. Mathai  Towards the fractional quantum Hall effect: a noncommutative geometry perspective
 R. Meyer  Homological algebra for Schwartz algebras of reductive \(p\)adic groups
 V. Nistor  A noncommutative geometry approach to the representation theory of reductive \(p\)adic groups: Homology of Hecke algebras, a survey and some new results
 F. Paugam  Three examples of noncommutative boundaries of Shimura varieties
 A. Polishchuk  Holomorphic bundles on 2dimensional noncommutative toric orbifolds
 R. Ponge  A new short proof of the local index formula of AtiyahSinger
