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Automorphic Representations and L-Functions for the General Linear Group: Volume 1: Cambridge Studies in Advanced Mathematics, cartea 129

Autor Dorian Goldfeld, Joseph Hundley
en Limba Engleză Hardback – 20 apr 2011
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.
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Specificații

ISBN-13: 9780521474238
ISBN-10: 052147423X
Pagini: 572
Ilustrații: 180 exercises
Dimensiuni: 152 x 229 x 37 mm
Greutate: 0.93 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Studies in Advanced Mathematics

Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

'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 MATH

Notă biografică


Descriere

This modern, graduate-level textbook does not assume prior knowledge of representation theory. Includes numerous concrete examples and over 250 exercises.