Automorphic Representations and L-Functions for the General Linear Group: Volume 1

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

Dorian Goldfeld (Author), Joseph Hundley (Author)

9780521474238, Cambridge University Press

Hardback, published 21 April 2011

572 pages, 180 exercises
22.9 x 15.2 x 3.7 cm, 1.01 kg

'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

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.

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.

Subject Areas: Number theory [PBH]