Automorphic Representations and L-Functions for the General Linear Group: Volume 2

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

Dorian Goldfeld (Author), Joseph Hundley (Author)

9781107007994, Cambridge University Press

Hardback, published 21 April 2011

210 pages, 55 exercises
22.9 x 15.2 x 1.3 cm, 0.45 kg

"Much of the material presented here is not easily available elsewhere. This brief volume will be of value to mathematicians seeking an introduction to the theory of automorphic forms, automorphic representationa, and L-functions."
Solomon Friedberg for Mathematical Reviews

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. The classical theory of automorphic forms for GL(n,R)
2. Automorphic forms and representations for GL(n,AQ)
3. Theory of local representations for GL(n)
4. The Godement–Jacquet L-function for GL(n,AQ)
Solutions to selected exercises
References
Symbols index
Index.

Subject Areas: Number theory [PBH]