Modern Analysis Of Automorphic Forms By Example Volume 2

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Modern Analysis of Automorphic Forms By Example: Volume 2

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Author : Paul Garrett
Publisher : Cambridge University Press
ISBN 13 : 1108669212
Total Pages : 367 pages
Book Rating : 4.1/5 (86 download)

Book Synopsis Modern Analysis of Automorphic Forms By Example: Volume 2 by : Paul Garrett

Download or read book Modern Analysis of Automorphic Forms By Example: Volume 2 written by Paul Garrett and published by Cambridge University Press. This book was released on 2018-09-20 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: Volume 1

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Author : Paul Garrett
Publisher : Cambridge University Press
ISBN 13 : 1108228240
Total Pages : 407 pages
Book Rating : 4.1/5 (82 download)

Book Synopsis Modern Analysis of Automorphic Forms By Example: Volume 1 by : Paul Garrett

Download or read book Modern Analysis of Automorphic Forms By Example: Volume 1 written by Paul Garrett and published by Cambridge University Press. This book was released on 2018-09-20 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Author : Paul Garrett
Publisher : Cambridge University Press
ISBN 13 : 9781107154001
Total Pages : 0 pages
Book Rating : 4.1/5 (54 download)

Book Synopsis Modern Analysis of Automorphic Forms By Example by : Paul Garrett

Download or read book Modern Analysis of Automorphic Forms By Example written by Paul Garrett and published by Cambridge University Press. This book was released on 2018-09-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Author : Paul Garrett
Publisher : Cambridge University Press
ISBN 13 : 1108473849
Total Pages : 367 pages
Book Rating : 4.1/5 (84 download)

Book Synopsis Modern Analysis of Automorphic Forms By Example by : Paul Garrett

Download or read book Modern Analysis of Automorphic Forms By Example written by Paul Garrett and published by Cambridge University Press. This book was released on 2018-09-20 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

An Introduction to Automorphic Representations

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Author : Jayce R. Getz
Publisher : Springer Nature
ISBN 13 : 3031411536
Total Pages : 611 pages
Book Rating : 4.0/5 (314 download)

Book Synopsis An Introduction to Automorphic Representations by : Jayce R. Getz

Download or read book An Introduction to Automorphic Representations written by Jayce R. Getz and published by Springer Nature. This book was released on with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Enumerative Combinatorics: Volume 2

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Author : Richard Stanley
Publisher : Cambridge University Press
ISBN 13 : 1009262513
Total Pages : 802 pages
Book Rating : 4.0/5 (92 download)

Book Synopsis Enumerative Combinatorics: Volume 2 by : Richard Stanley

Download or read book Enumerative Combinatorics: Volume 2 written by Richard Stanley and published by Cambridge University Press. This book was released on 2023-07-31 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 144714435X
Total Pages : 255 pages
Book Rating : 4.4/5 (471 download)

Book Synopsis Automorphic Forms by : Anton Deitmar

Download or read book Automorphic Forms written by Anton Deitmar and published by Springer Science & Business Media. This book was released on 2012-08-29 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms on Adele Groups. (AM-83), Volume 83

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Author : Stephen S. Gelbart
Publisher : Princeton University Press
ISBN 13 : 1400881617
Total Pages : 227 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Automorphic Forms on Adele Groups. (AM-83), Volume 83 by : Stephen S. Gelbart

Download or read book Automorphic Forms on Adele Groups. (AM-83), Volume 83 written by Stephen S. Gelbart and published by Princeton University Press. This book was released on 2016-03-02 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Automorphic Forms and Galois Representations: Volume 2

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Author : Fred Diamond
Publisher : Cambridge University Press
ISBN 13 : 1316062341
Total Pages : 387 pages
Book Rating : 4.3/5 (16 download)

Book Synopsis Automorphic Forms and Galois Representations: Volume 2 by : Fred Diamond

Download or read book Automorphic Forms and Galois Representations: Volume 2 written by Fred Diamond and published by Cambridge University Press. This book was released on 2014-10-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.

Automorphic Forms on Adele Groups

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Author : Stephen S. Gelbart
Publisher : Princeton University Press
ISBN 13 : 9780691081564
Total Pages : 0 pages
Book Rating : 4.0/5 (815 download)

Book Synopsis Automorphic Forms on Adele Groups by : Stephen S. Gelbart

Download or read book Automorphic Forms on Adele Groups written by Stephen S. Gelbart and published by Princeton University Press. This book was released on 1975-03-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Automorphic Forms on SL2 (R)

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Author : Armand Borel
Publisher : Cambridge University Press
ISBN 13 : 1316582639
Total Pages : 204 pages
Book Rating : 4.3/5 (165 download)

Book Synopsis Automorphic Forms on SL2 (R) by : Armand Borel

Download or read book Automorphic Forms on SL2 (R) written by Armand Borel and published by Cambridge University Press. This book was released on 1997-08-28 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book.

Eisenstein Series and Automorphic Representations

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Author : Philipp Fleig
Publisher : Cambridge Studies in Advanced
ISBN 13 : 1107189926
Total Pages : 587 pages
Book Rating : 4.1/5 (71 download)

Book Synopsis Eisenstein Series and Automorphic Representations by : Philipp Fleig

Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig and published by Cambridge Studies in Advanced. This book was released on 2018-07-05 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Contributions to Automorphic Forms, Geometry, and Number Theory

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Author : Haruzo Hida
Publisher : JHU Press
ISBN 13 : 9780801878602
Total Pages : 946 pages
Book Rating : 4.8/5 (786 download)

Book Synopsis Contributions to Automorphic Forms, Geometry, and Number Theory by : Haruzo Hida

Download or read book Contributions to Automorphic Forms, Geometry, and Number Theory written by Haruzo Hida and published by JHU Press. This book was released on 2004-03-11 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.

Spectral Methods of Automorphic Forms

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Author : Henryk Iwaniec
Publisher : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
ISBN 13 : 1470466228
Total Pages : 220 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Spectral Methods of Automorphic Forms by : Henryk Iwaniec

Download or read book Spectral Methods of Automorphic Forms written by Henryk Iwaniec and published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain. This book was released on 2021-11-17 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.

Automorphic Forms on GL (2)

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Author : H. Jacquet
Publisher : Springer
ISBN 13 : 9783540059318
Total Pages : 148 pages
Book Rating : 4.0/5 (593 download)

Book Synopsis Automorphic Forms on GL (2) by : H. Jacquet

Download or read book Automorphic Forms on GL (2) written by H. Jacquet and published by Springer. This book was released on 1972-07-28 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Decomposition and Eisenstein Series

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Author : Colette Moeglin
Publisher : Cambridge University Press
ISBN 13 : 9780521418935
Total Pages : 382 pages
Book Rating : 4.4/5 (189 download)

Book Synopsis Spectral Decomposition and Eisenstein Series by : Colette Moeglin

Download or read book Spectral Decomposition and Eisenstein Series written by Colette Moeglin and published by Cambridge University Press. This book was released on 1995-11-02 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms on Gl (2)

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Author : H. Jacquet
Publisher :
ISBN 13 : 9783662205877
Total Pages : 164 pages
Book Rating : 4.2/5 (58 download)

Book Synopsis Automorphic Forms on Gl (2) by : H. Jacquet

Download or read book Automorphic Forms on Gl (2) written by H. Jacquet and published by . This book was released on 2014-09-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: