Smooth Automorphic Forms And Smooth Automorphic Representations

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Smooth-automorphic Forms And Smooth-automorphic Representations

Harald Grobner
Smooth automorphic Forms And Smooth automorphic Representations Book PDF

Author : Harald Grobner
Publisher : World Scientific
Page : 262 pages
File Size : 45,7 Mb
Release : 2023-06-09
Category : Mathematics
ISBN : 9789811246180

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Smooth-automorphic Forms And Smooth-automorphic Representations by Harald Grobner Pdf

This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider 'K-finite' automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of 'smooth-automorphic forms' is intrinsic to the group scheme G/F.This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G.Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail.

Automorphic Forms and Representations

Daniel Bump
Automorphic Forms and Representations Book PDF

Author : Daniel Bump
Publisher : Cambridge University Press
Page : 592 pages
File Size : 43,7 Mb
Release : 1998-11-28
Category : Mathematics
ISBN : 0521658187

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Automorphic Forms and Representations by Daniel Bump Pdf

This book takes advanced graduate students from the foundations to topics on the research frontier.

Automorphic Representations and L-Functions for the General Linear Group: Volume 2

Dorian Goldfeld,Joseph Hundley
Automorphic Representations and L Functions for the General Linear Group Volume 2 Book PDF

Author : Dorian Goldfeld,Joseph Hundley
Publisher : Cambridge University Press
Page : 209 pages
File Size : 42,6 Mb
Release : 2011-04-21
Category : Mathematics
ISBN : 9781139503082

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Automorphic Representations and L-Functions for the General Linear Group: Volume 2 by Dorian Goldfeld,Joseph Hundley Pdf

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

Automorphic Forms, Representations and $L$-Functions

Armand Borel,W. Casselman,Bill Casselman,American Mathematical Society
Automorphic Forms Representations and L Functions Book PDF

Author : Armand Borel,W. Casselman,Bill Casselman,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 336 pages
File Size : 50,9 Mb
Release : 1979
Category : Mathematics
ISBN : 0821814745

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Automorphic Forms, Representations and $L$-Functions by Armand Borel,W. Casselman,Bill Casselman,American Mathematical Society Pdf

This was the conference on $L$-functions and automorphic forms.

Lectures on Automorphic L-functions

James W. Cogdell,Henry H. Kim,James W. Cogdell, Henry H. Kim, and M. Ram Murty,M. Ram Murty
Lectures on Automorphic L functions Book PDF

Author : James W. Cogdell,Henry H. Kim,James W. Cogdell, Henry H. Kim, and M. Ram Murty,M. Ram Murty
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 46,6 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 082187179X

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Lectures on Automorphic L-functions by James W. Cogdell,Henry H. Kim,James W. Cogdell, Henry H. Kim, and M. Ram Murty,M. Ram Murty Pdf

James W. Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$: Preface Modular forms and their $L$-functions Automorphic forms Automorphic representations Fourier expansions and multiplicity one theorems Eulerian integral representations Local $L$-functions: The non-Archimedean case The unramified calculation Local $L$-functions: The Archimedean case Global $L$-functions Converse theorems Functoriality Functoriality for the classical groups Functoriality for the classical groups, II Henry H. Kim, Automorphic $L$-functions: Introduction Chevalley groups and their properties Cuspidal representations $L$-groups and automorphic $L$-functions Induced representations Eisenstein series and constant terms $L$-functions in the constant terms Meromorphic continuation of $L$-functions Generic representations and their Whittaker models Local coefficients and non-constant terms Local Langlands correspondence Local $L$-functions and functional equations Normalization of intertwining operators Holomorphy and bounded in vertical strips Langlands functoriality conjecture Converse theorem of Cogdell and Piatetski-Shapiro Functoriality of the symmetric cube Functoriality of the symmetric fourth Bibliography M. Ram Murty, Applications of symmetric power $L$-functions: Preface The Sato-Tate conjecture Maass wave forms The Rankin-Selberg method Oscillations of Fourier coefficients of cusp forms Poincare series Kloosterman sums and Selberg's conjecture Refined estimates for Fourier coefficients of cusp forms Twisting and averaging of $L$-series The Kim-Sarnak theorem Introduction to Artin $L$-functions Zeros and poles of Artin $L$-functions The Langlands-Tunnell theorem Bibliography

Automorphic Forms on GL (2)

H. Jacquet
Automorphic Forms on GL 2 Book PDF

Author : H. Jacquet
Publisher : Springer
Page : 156 pages
File Size : 48,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540376125

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Automorphic Forms on GL (2) by H. Jacquet Pdf

Automorphic Forms, Representations and $L$-Functions

A. Borel,W. Casselman
Automorphic Forms Representations and L Functions Book PDF

Author : A. Borel,W. Casselman
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 53,8 Mb
Release : 1979
Category : Mathematics
ISBN : 9780821814352

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Automorphic Forms, Representations and $L$-Functions by A. Borel,W. Casselman Pdf

Contains sections on Reductive groups, representations, Automorphic forms and representations.

Representation Theory and Automorphic Forms

T. N. Bailey,Anthony W. Knapp
Representation Theory and Automorphic Forms Book PDF

Author : T. N. Bailey,Anthony W. Knapp
Publisher : American Mathematical Soc.
Page : 490 pages
File Size : 55,6 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806098

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Representation Theory and Automorphic Forms by T. N. Bailey,Anthony W. Knapp Pdf

The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR

Automorphic Representations of Unitary Groups in Three Variables

Jonathan David Rogawski
Automorphic Representations of Unitary Groups in Three Variables Book PDF

Author : Jonathan David Rogawski
Publisher : Princeton University Press
Page : 272 pages
File Size : 40,6 Mb
Release : 1990-09-21
Category : Mathematics
ISBN : 9780691085876

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Automorphic Representations of Unitary Groups in Three Variables by Jonathan David Rogawski Pdf

The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.

Smooth-Automorphic Forms and Smooth-Automorphic Representations

Harald Grobner
Smooth Automorphic Forms and Smooth Automorphic Representations Book PDF

Author : Harald Grobner
Publisher : World Scientific Publishing Company
Page : 0 pages
File Size : 52,5 Mb
Release : 2023-07-30
Category : Mathematics
ISBN : 9811246165

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Smooth-Automorphic Forms and Smooth-Automorphic Representations by Harald Grobner Pdf

This book provides a thorough introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F. Our approach to automorphic representations is, however, different to what one usually finds in the literature: We do not restrict ourselves to considering K-finite automorphic forms, but allow a richer class of only smooth functions. In this way, we regain a perfect symmetry between the archimedean and the non-archimedean places of our number field F, making our bigger space of smooth automorphic forms a proper, continuous representation of the full group of adelic points of G. This book is a unique source, where a theory of smooth automorphic representations is developed and presented in great detail.

An Introduction to Automorphic Representations

Jayce R. Getz
An Introduction to Automorphic Representations Book PDF

Author : Jayce R. Getz
Publisher : Springer Nature
Page : 611 pages
File Size : 52,9 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031411533

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An Introduction to Automorphic Representations by Jayce R. Getz Pdf

Automorphic Forms on Adele Groups

Stephen S. Gelbart
Automorphic Forms on Adele Groups Book PDF

Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 279 pages
File Size : 42,7 Mb
Release : 1975-03-21
Category : Mathematics
ISBN : 9780691081564

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Automorphic Forms on Adele Groups by Stephen S. Gelbart Pdf

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?

Contributions to Automorphic Forms, Geometry, and Number Theory

Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi
Contributions to Automorphic Forms Geometry and Number Theory Book PDF

Author : Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi
Publisher : JHU Press
Page : 946 pages
File Size : 46,6 Mb
Release : 2004-03-11
Category : Mathematics
ISBN : 0801878608

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Contributions to Automorphic Forms, Geometry, and Number Theory by Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi Pdf

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.