Automorphic Forms Beyond Mathrm Gl 2 PDF Download
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Author | : Ellen Elizabeth Eischen |
Publisher | : American Mathematical Society |
Total Pages | : 199 |
Release | : 2024-03-26 |
Genre | : Mathematics |
ISBN | : 1470474921 |
Download Automorphic Forms Beyond $mathrm {GL}_2$ Book in PDF, ePub and Kindle
The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.
Author | : H. Jacquet |
Publisher | : |
Total Pages | : 564 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662204016 |
Download Automorphic Forms on Gl (2) Book in PDF, ePub and Kindle
Author | : H. Jacquet |
Publisher | : Springer |
Total Pages | : 156 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540376127 |
Download Automorphic Forms on GL (2) Book in PDF, ePub and Kindle
Author | : H. Jacquet |
Publisher | : |
Total Pages | : 164 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9783662205877 |
Download Automorphic Forms on Gl (2) Book in PDF, ePub and Kindle
Author | : Hervé Jacquet |
Publisher | : |
Total Pages | : 888 |
Release | : 1970 |
Genre | : Automorphic forms |
ISBN | : |
Download Automorphic Forms on GL (2) Book in PDF, ePub and Kindle
Author | : Hervé Jacquet |
Publisher | : |
Total Pages | : 548 |
Release | : 1970 |
Genre | : Automorphic forms |
ISBN | : |
Download Automorphic Forms on GL(2) Vol. I Book in PDF, ePub and Kindle
Author | : Stephen S. Gelbart |
Publisher | : Princeton University Press |
Total Pages | : 284 |
Release | : 1975-03-21 |
Genre | : Mathematics |
ISBN | : 9780691081564 |
Download Automorphic Forms on Adele Groups Book in PDF, ePub and Kindle
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?
Author | : Stephen S. Gelbart |
Publisher | : Princeton University Press |
Total Pages | : 227 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881617 |
Download Automorphic Forms on Adele Groups. (AM-83), Volume 83 Book in PDF, ePub and Kindle
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?
Author | : Jonathan David Rogawski |
Publisher | : Princeton University Press |
Total Pages | : 272 |
Release | : 1990-09-21 |
Genre | : Mathematics |
ISBN | : 0691085870 |
Download Automorphic Representations of Unitary Groups in Three Variables Book in PDF, ePub and Kindle
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.
Author | : Yuval Z. Flicker |
Publisher | : World Scientific |
Total Pages | : 340 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 9812703322 |
Download Automorphic Forms and Shimura Varieties of PGSp (2) Book in PDF, ePub and Kindle
The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftings.OCO This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to LanglandsOCO program in the area of automorphic representations. It includes a proof of known cases of ArtinOCOs conjecture."