Author: John Coates
Publisher:
ISBN: 9781316254554
Category : Functions, Zeta
Languages : en
Pages : 317
Book Description
The Bloch-Kato Conjecture for the Riemann Zeta Function
Author: John Coates
Publisher:
ISBN: 9781316254554
Category : Functions, Zeta
Languages : en
Pages : 317
Book Description
Publisher:
ISBN: 9781316254554
Category : Functions, Zeta
Languages : en
Pages : 317
Book Description
The Bloch–Kato Conjecture for the Riemann Zeta Function
Author: John Coates
Publisher: Cambridge University Press
ISBN: 1316241300
Category : Mathematics
Languages : en
Pages : 317
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.
Publisher: Cambridge University Press
ISBN: 1316241300
Category : Mathematics
Languages : en
Pages : 317
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.
The Bloch-Kato Conjecture for the Riemann Zeta Function
Author: John Coates
Publisher:
ISBN: 9781316250761
Category : Functions, Zeta
Languages : en
Pages : 305
Book Description
A graduate-level account of an important recent result concerning the Riemann zeta function.
Publisher:
ISBN: 9781316250761
Category : Functions, Zeta
Languages : en
Pages : 305
Book Description
A graduate-level account of an important recent result concerning the Riemann zeta function.
Exploring the Riemann Zeta Function
Author: Hugh Montgomery
Publisher: Springer
ISBN: 3319599690
Category : Mathematics
Languages : en
Pages : 300
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.
Publisher: Springer
ISBN: 3319599690
Category : Mathematics
Languages : en
Pages : 300
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.
Zeta and L-Functions of Varieties and Motives
Author: Bruno Kahn
Publisher: Cambridge University Press
ISBN: 1108574912
Category : Mathematics
Languages : en
Pages : 217
Book Description
The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.
Publisher: Cambridge University Press
ISBN: 1108574912
Category : Mathematics
Languages : en
Pages : 217
Book Description
The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.
Lectures on Orthogonal Polynomials and Special Functions
Author: Howard S. Cohl
Publisher: Cambridge University Press
ISBN: 1108821596
Category : Mathematics
Languages : en
Pages : 351
Book Description
Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Publisher: Cambridge University Press
ISBN: 1108821596
Category : Mathematics
Languages : en
Pages : 351
Book Description
Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Invariance of Modules under Automorphisms of their Envelopes and Covers
Author: Ashish K. Srivastava
Publisher: Cambridge University Press
ISBN: 1108960162
Category : Mathematics
Languages : en
Pages : 235
Book Description
The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.
Publisher: Cambridge University Press
ISBN: 1108960162
Category : Mathematics
Languages : en
Pages : 235
Book Description
The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.
Differential Geometry in the Large
Author: Owen Dearricott
Publisher: Cambridge University Press
ISBN: 1108812813
Category : Mathematics
Languages : en
Pages : 401
Book Description
From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
Publisher: Cambridge University Press
ISBN: 1108812813
Category : Mathematics
Languages : en
Pages : 401
Book Description
From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
(Co)end Calculus
Author: Fosco Loregian
Publisher: Cambridge University Press
ISBN: 1108746128
Category : Mathematics
Languages : en
Pages : 331
Book Description
This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.
Publisher: Cambridge University Press
ISBN: 1108746128
Category : Mathematics
Languages : en
Pages : 331
Book Description
This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.
The Genesis of the Langlands Program
Author: Julia Mueller
Publisher: Cambridge University Press
ISBN: 1108619959
Category : Mathematics
Languages : en
Pages : 452
Book Description
Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.
Publisher: Cambridge University Press
ISBN: 1108619959
Category : Mathematics
Languages : en
Pages : 452
Book Description
Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.