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Modern Analysis Of Automorphic Forms By Example


Modern Analysis Of Automorphic Forms By Example
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Modern Analysis Of Automorphic Forms By Example


Modern Analysis Of Automorphic Forms By Example
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Author : Paul Garrett
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-20

Modern Analysis Of Automorphic Forms By Example written by Paul Garrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.


Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.



Modern Analysis Of Automorphic Forms By Example Volume 2


Modern Analysis Of Automorphic Forms By Example Volume 2
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Author : Paul Garrett
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-20

Modern Analysis Of Automorphic Forms By Example Volume 2 written by Paul Garrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.


This is Volume 2 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 2 features critical results, which are proven carefully and in detail, including automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. Volume 1 features discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.



Modern Analysis Of Automorphic Forms By Example


Modern Analysis Of Automorphic Forms By Example
DOWNLOAD
Author : Paul Garrett
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-20

Modern Analysis Of Automorphic Forms By Example written by Paul Garrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.


This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.



Modern Analysis Of Automorphic Forms By Example


Modern Analysis Of Automorphic Forms By Example
DOWNLOAD
Author : Paul Garrett
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-20

Modern Analysis Of Automorphic Forms By Example written by Paul Garrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.


Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.



Eisenstein Series And Automorphic Representations


Eisenstein Series And Automorphic Representations
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Author : Philipp Fleig
language : en
Publisher: Cambridge Studies in Advanced
Release Date : 2018-07-05

Eisenstein Series And Automorphic Representations written by Philipp Fleig and has been published by Cambridge Studies in Advanced this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Mathematics categories.


Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.



An Introduction To Automorphic Representations


An Introduction To Automorphic Representations
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Author : Jayce R. Getz
language : en
Publisher: Springer Nature
Release Date : 2024-03-01

An Introduction To Automorphic Representations written by Jayce R. Getz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-01 with Mathematics categories.


The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics. The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields. The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed. This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface.



Functional Analysis


Functional Analysis
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Author : Jan van Neerven
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-07

Functional Analysis written by Jan van Neerven and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-07 with Mathematics categories.


This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.



Homological Theory Of Representations


Homological Theory Of Representations
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Author : Henning Krause
language : en
Publisher: Cambridge University Press
Release Date : 2021-11-18

Homological Theory Of Representations written by Henning Krause and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Mathematics categories.


This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.



Generators Of Markov Chains


Generators Of Markov Chains
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Author : Adam Bobrowski
language : en
Publisher: Cambridge University Press
Release Date : 2021

Generators Of Markov Chains written by Adam Bobrowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.


A clear explanation of what an explosive Markov chain does after it passes through all available states in finite time.



Higher Index Theory


Higher Index Theory
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Author : Rufus Willett
language : en
Publisher: Cambridge University Press
Release Date : 2020-07-02

Higher Index Theory written by Rufus Willett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Mathematics categories.


A friendly introduction to higher index theory, a rapidly-developing subject at the intersection of geometry, topology and operator algebras. A well-balanced combination of introductory material (with exercises), cutting-edge developments and references to the wider literature make this book a valuable guide for graduate students and experts alike.