The Bloch-Kato Conjecture for the Riemann Zeta Function PDF Download
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Author: John Coates
Publisher:
ISBN: 9781316254554
Category : Functions, Zeta
Languages : en
Pages : 317
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Book Description
Author: John Coates
Publisher:
ISBN: 9781316254554
Category : Functions, Zeta
Languages : en
Pages : 317
Get Book Here
Book Description
Author: John Coates
Publisher: Cambridge University Press
ISBN: 1316241300
Category : Mathematics
Languages : en
Pages : 317
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Book Description
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.
Author: John Coates
Publisher:
ISBN: 9781316250761
Category : Functions, Zeta
Languages : en
Pages : 305
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Book Description
A graduate-level account of an important recent result concerning the Riemann zeta function.
Author: Hugh Montgomery
Publisher: Springer
ISBN: 3319599690
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.
Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 1108715745
Category : Mathematics
Languages : en
Pages : 421
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Book Description
A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
Author: Thomas Haines
Publisher: Cambridge University Press
ISBN: 1108704867
Category : Mathematics
Languages : en
Pages : 341
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Book Description
This volume forms the sequel to "On the stabilization of the trace formula", published by International Press of Boston, Inc., 2011
Author: Mark Pankov
Publisher: Cambridge University Press
ISBN: 1108848397
Category : Mathematics
Languages : en
Pages : 155
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Book Description
Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.
Author: N. Broaddus
Publisher: Cambridge University Press
ISBN: 1108530508
Category : Mathematics
Languages : en
Pages : 211
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Book Description
This volume collects the proceedings of the conference 'Topological methods in group theory', held at Ohio State University in 2014 in honor of Ross Geoghegan's 70th birthday. It consists of eleven peer-reviewed papers on some of the most recent developments at the interface of topology and geometric group theory. The authors have given particular attention to clear exposition, making this volume especially useful for graduate students and for mathematicians in other areas interested in gaining a taste of this rich and active field. A wide cross-section of topics in geometric group theory and topology are represented, including left-orderable groups, groups defined by automata, connectivity properties and Σ-invariants of groups, amenability and non-amenability problems, and boundaries of certain groups. Also included are topics that are more geometric or topological in nature, such as the geometry of simplices, decomposition complexity of certain groups, and problems in shape theory.
Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 110880358X
Category : Mathematics
Languages : en
Pages : 421
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Book Description
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.
Author: Kai Liu
Publisher: Cambridge University Press
ISBN: 1108705170
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Presents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.
