Automorphic Representations and L-Functions for the General Linear Group: Volume 1
1st Edition
Published on 24. May 2011
978-1-139-06469-9 (ISBN)
Description
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.
Reviews / Votes
'In this book, the authors give a thorough yet elementary introduction to the theory of automorphic forms and L-functions for the general linear group of rank two over rational adeles ... The exposition is accompanied by exercises after every chapter. Definitions are repeated when needed, and previous results are always cited, so the book is very accessible.' Marcela Hanzer, Zentralblatt MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
3,43 MB
ISBN-13
978-1-139-06469-9 (9781139064699)
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Schweitzer Classification
Other editions
Additional editions
Dorian Goldfeld | Joseph Hundley
Automorphic Representations and L-Functions for the General Linear Group: Volume 1
Book
04/2011
Cambridge University Press
€164.40
Shipment within 15-20 days
Persons
Dorian Goldfeld is a Professor in the Department of Mathematics at Columbia University, New York. Joseph Hundley is an Assistant Professor in the Department of Mathematics at Southern Illinois University, Carbondale.
Content
Preface; 1. Adeles over Q; 2. Automorphic representations and L-functions for GL(1,AQ); 3. The classical theory of automorphic forms for GL(2); 4. Automorphic forms for GL(2,AQ); 5. Automorphic representations for GL(2,AQ); 6. Theory of admissible representations of GL(2,Qp); 7. Theory of admissible (g,K?) modules for GL(2,R); 8. The contragredient representation for GL(2); 9. Unitary representations of GL(2); 10. Tensor products of local representations; 11. The Godement-Jacquet L-function for GL(2,AQ); Solutions to selected exercises; References; Symbols index; Index.
