Automorphic Representations and L-Functions for the General Linear Group
Automorphic Representations and L-Functions for the General Linear Group
Joseph Hundley, Southern Illinois University, Carbondale
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(C) USDThis 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.
- Presents clear, detailed proofs suitable for graduate students
- Immediately engages students using simple, concrete examples
- Contains numerous exercises with solutions
Reviews & endorsements
"This book treats the subject without imposing many prerequisites, and the pace is leisurely throughout. The authors also make an effort to explain every term. Accordingly, students are likely to find it quite accessible."
Solomon Friedberg for Mathematical Reviews
Product details
May 2011Hardback
9780521474238
572 pages
229 × 152 × 37 mm
1.01kg
180 exercises
Available
Table of Contents
- 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.
