The Bloch–Kato Conjecture for the Riemann Zeta Function

Nonfiction, Science & Nature, Mathematics, Number Theory, Algebra
Cover of the book The Bloch–Kato Conjecture for the Riemann Zeta Function by , Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9781316235638
Publisher: Cambridge University Press Publication: March 19, 2015
Imprint: Cambridge University Press Language: English
Author:
ISBN: 9781316235638
Publisher: Cambridge University Press
Publication: March 19, 2015
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book The International Atlas of Mars Exploration: Volume 2, 2004 to 2014 by
Cover of the book Women Prophets and Radical Protestantism in the British Atlantic World, 1640–1730 by
Cover of the book Towards a Cultural Politics of Climate Change by
Cover of the book The Gacaca Courts, Post-Genocide Justice and Reconciliation in Rwanda by
Cover of the book The Frigid Golden Age by
Cover of the book The Myth of Rome in Shakespeare and his Contemporaries by
Cover of the book Poetry, Media, and the Material Body by
Cover of the book Darkness Now Visible by
Cover of the book Modern Compiler Implementation in ML by
Cover of the book Drawn from the Ground by
Cover of the book International Negotiation by
Cover of the book The Collins Class Submarine Story by
Cover of the book The Cambridge Companion to Elizabeth Bishop by
Cover of the book The Cambridge Companion to Eighteenth-Century Opera by
Cover of the book Worker Absenteeism and Sick Pay by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy