Modern Analysis Of Automorphic Forms By Example Volume 2
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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 2 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
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Author : Paul Garrett
language : en
Publisher: Cambridge Studies in Advanced Mathematics
Release Date : 2018-09-20
Modern Analysis Of Automorphic Forms By Example written by Paul Garrett and has been published by Cambridge Studies in Advanced Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Automorphic forms categories.
"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"--Publisher's description.
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.
Enumerative Combinatorics Volume 2
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Author : Richard Stanley
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17
Enumerative Combinatorics Volume 2 written by Richard Stanley 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 2023-08-17 with Mathematics categories.
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.
Automorphic Forms
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Author : Anton Deitmar
language : en
Publisher: Springer
Release Date : 2012-08-29
Automorphic Forms written by Anton Deitmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.
Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory
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Author : Roger Howe
language : en
Publisher: World Scientific
Release Date : 2007
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory written by Roger Howe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume carries the same title as that of an international conference held at the National University of Singapore, 9OCo11 January 2006 on the occasion of Roger E. Howe''s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe''s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. Sample Chapter(s). Foreword (21 KB). Chapter 1: The Theta Correspondence Over R (342 KB). Contents: The Theta Correspondence over R (J Adams); The Heisenberg Group, SL (3, R), and Rigidity (A iap et al.); Pfaffians and Strategies for Integer Choice Games (R Evans & N Wallach); When is an L -Function Non-Vanishing in Part of the Critical Strip? (S Gelbart); Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L -Functions (M Harris); The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group (T Kobayashi & G Mano); Classification des S(r)ries Discr tes pour Certains Groupes Classiques p- Adiques (C Moeglin); Some Algebras of Essentially Compact Distributions of a Reductive p -Adic Group (A Moy & M Tadic); Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras (T Oshima); Branching to a Maximal Compact Subgroup (D A Vogan, Jr.); Small Semisimple Subalgebras of Semisimple Lie Algebras (J F Willenbring & G J Zuckerman). Readership: Graduate students and research mathematicians in harmonic analysis, group representations, automorphic forms and invariant theory."
Spectral Decomposition And Eisenstein Series
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Author : Colette Moeglin
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-02
Spectral Decomposition And Eisenstein Series written by Colette Moeglin 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 1995-11-02 with Mathematics categories.
A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.
In The Tradition Of Thurston Ii
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2022-08-02
In The Tradition Of Thurston Ii written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-02 with Mathematics categories.
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
Spectral Methods Of Automorphic Forms
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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Spectral Methods Of Automorphic Forms written by Henryk Iwaniec and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this volume was an underground classic, both as a textbook and as a respected source for results, ideas, and references. The book's reputation sparked a growing interest inthe mathematical community to bring it back into print. The AMS has answered that call with the publication of this second edition. In the book, Iwaniec treats the spectral theory of automorphic forms as the study of the space $L2 (H\Gamma)$, where $H$ is the upper half-plane and $\Gamma$ is a discretesubgroup of volume-preserving transformations of $H$. He combines various techniques from analytic number theory. Among the topics discussed are Eisenstein series, estimates for Fourier coefficients of automorphic forms, the theory of Kloosterman sums, the Selberg trace formula, and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 AMS Cole Prize for his fundamental contributions to analytic number theory. Also available from the AMS by H. Iwaniec is Topics in ClassicalAutomorphic Forms, Volume 17 in the Graduate Studies in Mathematics series. The book is designed for graduate students and researchers working in analytic number theory.
Mostly Surfaces
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Author : Richard Evan Schwartz
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Mostly Surfaces written by Richard Evan Schwartz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.