Smooth Automorphic Forms And Smooth Automorphic Representations

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Smooth-automorphic Forms And Smooth-automorphic Representations

Author : Harald Grobner
Publisher : World Scientific
ISBN 13 : 9811246181
Total Pages : 262 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Smooth-automorphic Forms And Smooth-automorphic Representations by : Harald Grobner

Download or read book Smooth-automorphic Forms And Smooth-automorphic Representations written by Harald Grobner and published by World Scientific. This book was released on 2023-06-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Daniel Bump
Publisher : Cambridge University Press
ISBN 13 : 9780521658188
Total Pages : 592 pages
Book Rating : 4.6/5 (581 download)

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Book Synopsis Automorphic Forms and Representations by : Daniel Bump

Download or read book Automorphic Forms and Representations written by Daniel Bump and published by Cambridge University Press. This book was released on 1998-11-28 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes advanced graduate students from the foundations to topics on the research frontier.

Smooth-Automorphic Forms and Smooth-Automorphic Representations

Author : Harald Grobner
Publisher : World Scientific Publishing Company
ISBN 13 : 9789811246166
Total Pages : 0 pages
Book Rating : 4.2/5 (461 download)

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Book Synopsis Smooth-Automorphic Forms and Smooth-Automorphic Representations by : Harald Grobner

Download or read book Smooth-Automorphic Forms and Smooth-Automorphic Representations written by Harald Grobner and published by World Scientific Publishing Company. This book was released on 2023-07-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms on GL (2)

Author : H. Jacquet
Publisher : Springer
ISBN 13 : 3540376127
Total Pages : 156 pages
Book Rating : 4.5/5 (43 download)

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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 2006-11-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Author : Dorian Goldfeld
Publisher : Cambridge University Press
ISBN 13 : 1139503081
Total Pages : 209 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Automorphic Representations and L-Functions for the General Linear Group: Volume 2 by : Dorian Goldfeld

Download or read book Automorphic Representations and L-Functions for the General Linear Group: Volume 2 written by Dorian Goldfeld and published by Cambridge University Press. This book was released on 2011-04-21 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Automorphic L-functions

Author : James W. Cogdell
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871799
Total Pages : 300 pages
Book Rating : 4.8/5 (717 download)

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Book Synopsis Lectures on Automorphic L-functions by : James W. Cogdell

Download or read book Lectures on Automorphic L-functions written by James W. Cogdell and published by American Mathematical Soc.. This book was released on with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Representations and $L$-Functions

Author : A. Borel
Publisher : American Mathematical Soc.
ISBN 13 : 0821814354
Total Pages : 334 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms, Representations and $L$-Functions by : A. Borel

Download or read book Automorphic Forms, Representations and $L$-Functions written by A. Borel and published by American Mathematical Soc.. This book was released on 1979 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Reductive groups, representations, Automorphic forms and representations.

Automorphic Forms, Representations and $L$-Functions

Author : Armand Borel
Publisher : American Mathematical Soc.
ISBN 13 : 9780821814741
Total Pages : 336 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Automorphic Forms, Representations and $L$-Functions by : Armand Borel

Download or read book Automorphic Forms, Representations and $L$-Functions written by Armand Borel and published by American Mathematical Soc.. This book was released on 1979 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This was the conference on $L$-functions and automorphic forms.

Representation Theory and Automorphic Forms

Author : T. N. Bailey
Publisher : American Mathematical Soc.
ISBN 13 : 0821806092
Total Pages : 490 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representation Theory and Automorphic Forms by : T. N. Bailey

Download or read book Representation Theory and Automorphic Forms written by T. N. Bailey and published by American Mathematical Soc.. This book was released on 1997 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Jonathan David Rogawski
Publisher : Princeton University Press
ISBN 13 : 0691085870
Total Pages : 272 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Automorphic Representations of Unitary Groups in Three Variables by : Jonathan David Rogawski

Download or read book Automorphic Representations of Unitary Groups in Three Variables written by Jonathan David Rogawski and published by Princeton University Press. This book was released on 1990-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms, Automorphic Representations, and Arithmetic

Author : Robert S. Doran
Publisher : American Mathematical Soc.
ISBN 13 : 0821810510
Total Pages : pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms, Automorphic Representations, and Arithmetic by : Robert S. Doran

Download or read book Automorphic Forms, Automorphic Representations, and Arithmetic written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Proceedings of Symposia in Pure Mathematics, Volume 33, Part 1

Author : A. Borel
Publisher : American Mathematical Soc.
ISBN 13 : 0821867911
Total Pages : 334 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Proceedings of Symposia in Pure Mathematics, Volume 33, Part 1 by : A. Borel

Download or read book Proceedings of Symposia in Pure Mathematics, Volume 33, Part 1 written by A. Borel and published by American Mathematical Soc.. This book was released on with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Automorphic Representations

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

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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:

Automorphic Forms on GL (3,TR)

Author : D. Bump
Publisher : Springer
ISBN 13 : 3540390553
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Automorphic Forms on GL (3,TR) by : D. Bump

Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Contributions to Automorphic Forms, Geometry, and Number Theory

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

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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.

The Descent Map from Automorphic Representations of GL(n) to Classical Groups

Author :
Publisher :
ISBN 13 : 9814464945
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis The Descent Map from Automorphic Representations of GL(n) to Classical Groups by :

Download or read book The Descent Map from Automorphic Representations of GL(n) to Classical Groups written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Descent Map from Automorphic Representations of GL(n) to Classical Groups

Author : David Ginzburg
Publisher : World Scientific
ISBN 13 : 9814304999
Total Pages : 350 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis The Descent Map from Automorphic Representations of GL(n) to Classical Groups by : David Ginzburg

Download or read book The Descent Map from Automorphic Representations of GL(n) to Classical Groups written by David Ginzburg and published by World Scientific. This book was released on 2011 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction. 1.1. Overview. 1.2. Formulas for the Weil representation. 1.3. The case, where H is unitary and the place v splits in E -- 2. On certain residual representations. 2.1. The groups. 2.2. The Eisenstein series to be considered. 2.3. L-groups and representations related to P[symbol]. 2.4. The residue representation. 2.5. The case of a maximal parabolic subgroup (r = 1). 2.6. A preliminary lemma on Eisenstein series on GL[symbol]. 2.7. Constant terms of E(h, f[symbol]). 2.8. Description of W(M[symbol], D[symbol]). 2.9. Continuation of the proff of Theorem 2.1 -- 3. Coefficients of Gelfand-Graev type, of Fourier-Jacobi type, and descent. 3.1. Gelfand-Graev coefficients. 3.2. Fourier-Jacobi coefficients. 3.3. Nilpotent orbits. 3.4. Global integrals representing L-functions I. 3.5. Global integrals representing L-functions II. 3.6. Definition of the descent. 3.7. Definition of Jacquet modules corresponding to Gelfand-Graev characters. 3.8. Definition of Jacquet modules corresponding to Fourier-Jacobi characters -- 4. Some double coset decompositions. 4.1. The space Q[symbol]. 4.2. A set of representatives for Q[symbol]. 4.3. Stabilizers. 4.4. The set Q\h[symbol] -- 5. Jacquet modules of parabolic inductions : Gelfand-Graev characters. 5.1. The case where K is a field. 5.2. The case K = k[symbol]k -- 6. Jacquet modules of parabolic inductions : Fourier-Jacobi characters. 6.1. The case where K is a field. 6.2. The case K = k[symbol]k -- 7. The tower property. 7.1. A general lemma on "exchanging roots". 7.2. A formula for constant terms of Gelfand-Graev coefficients. 7.3. Global Gelfand-Graev models for cuspidal representations. 7.4. The general case : H is neither split nor quasi-split. 7.5. Global Gelfand-Graev models for the residual representations E[symbol]. 7.6. A formula for constant terms of Fourier-Jacobi coefficients. 7.7. Global Fourier-Jacobi models for cuspidal representations. 7.8. Global Fourier-Jacobi models for the residual representations E[symbol]