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Author : Jayce R. Getz
Publisher : Springer Nature
Page : 611 pages
File Size : 52,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031411533
Author : D. Bump
Publisher : Springer
Page : 196 pages
File Size : 51,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540390558
Author : H. Jacquet
Publisher : Springer
Page : 156 pages
File Size : 51,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540376125
Author : Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 40,7 Mb
Release : 2007-10-10
Category : Mathematics
ISBN : 9780817646462
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 : Harald Grobner
Publisher : World Scientific
Page : 262 pages
File Size : 52,6 Mb
Release : 2023-06-09
Category : Mathematics
ISBN : 9789811246180
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.
Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 227 pages
File Size : 43,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881611
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
Page : 255 pages
File Size : 53,6 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9781447144359
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 : James W. Cogdell,Dihua Jiang,Stephen S. Kudla,David Soudry,Robert J. Stanton
Publisher : Walter de Gruyter
Page : 441 pages
File Size : 48,9 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110892703
This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.
Author : Philipp Fleig,Henrik P. A. Gustafsson,Axel Kleinschmidt,Daniel Persson
Publisher : Cambridge Studies in Advanced
Page : 587 pages
File Size : 54,9 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9781107189928
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author : Armand Borel,W. Casselman,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 49,5 Mb
Release : 1979-06-30
Category : Mathematics
ISBN : 9780821814376
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Author : Volker Heiermann,Dipendra Prasad
Publisher : Springer
Page : 364 pages
File Size : 49,8 Mb
Release : 2018-10-01
Category : Mathematics
ISBN : 9783319952314
This volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers. Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the Jacquet–Langlands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize Godement–Jacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups. The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.
Author : Jonathan David Rogawski
Publisher : Princeton University Press
Page : 272 pages
File Size : 42,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882441
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 : Jian-Shu Li
Publisher : World Scientific
Page : 446 pages
File Size : 48,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770783
This volume carries the same title as that of an international conference held at the National University of Singapore, 9-11 January 2006 on the occasion of Roger E. Howe's 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe's mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications.
Author : Jonathan David Rogawski
Publisher : Princeton University Press
Page : 272 pages
File Size : 55,7 Mb
Release : 1990-09-21
Category : Mathematics
ISBN : 9780691085876
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 : Joseph Bernstein,Stephen Gelbart
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 41,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9780817682262
This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
