The Bloch–Kato Conjecture for the Riemann Zeta Function
John Coates editor R Sujatha editor A Raghuram editor Anupam Saikia editor
Format:Paperback
Publisher:Cambridge University Press
Published:13th Mar '15
Currently unavailable, and unfortunately no date known when it will be back
A graduate-level account of an important recent result concerning the Riemann zeta function.
An account of a significant body of recent work that resolves some long-standing mysteries concerning special values of the Riemann zeta function. It brings together many important results from K-theory, motivic cohomology, and Iwasawa theory, accessible at graduate level and above.There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
ISBN: 9781107492967
Dimensions: 228mm x 153mm x 18mm
Weight: 460g
320 pages