An Introduction to Automorphic Representations
Author | : Jayce R. Getz |
Publisher | : Springer Nature |
Total Pages | : 611 |
Release | : |
Genre | : |
ISBN | : 3031411536 |
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Author | : Jayce R. Getz |
Publisher | : Springer Nature |
Total Pages | : 611 |
Release | : |
Genre | : |
ISBN | : 3031411536 |
Author | : D. Bump |
Publisher | : Springer |
Total Pages | : 196 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540390553 |
Author | : Armand Borel |
Publisher | : American Mathematical Soc. |
Total Pages | : 394 |
Release | : 1979-06-30 |
Genre | : Mathematics |
ISBN | : 0821814370 |
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Author | : H. Jacquet |
Publisher | : Springer |
Total Pages | : 156 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540376127 |
Author | : Toshiyuki Kobayashi |
Publisher | : Springer Science & Business Media |
Total Pages | : 220 |
Release | : 2007-10-10 |
Genre | : Mathematics |
ISBN | : 0817646469 |
This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.
Author | : Philipp Fleig |
Publisher | : Cambridge Studies in Advanced |
Total Pages | : 587 |
Release | : 2018-07-05 |
Genre | : Mathematics |
ISBN | : 1107189926 |
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author | : Stephen S. Gelbart |
Publisher | : Princeton University Press |
Total Pages | : 227 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881617 |
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 | : Anton Deitmar |
Publisher | : Springer Science & Business Media |
Total Pages | : 255 |
Release | : 2012-08-29 |
Genre | : Mathematics |
ISBN | : 144714435X |
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.
Author | : David Soudry |
Publisher | : World Scientific |
Total Pages | : 350 |
Release | : 2011-06-30 |
Genre | : Mathematics |
ISBN | : 9814464945 |
This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of Gelfand-Graev type, or of Fourier-Jacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.
Author | : Harald Grobner |
Publisher | : World Scientific |
Total Pages | : 262 |
Release | : 2023-06-09 |
Genre | : Mathematics |
ISBN | : 9811246181 |
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.