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.
- Presents clear, detailed proofs suitable for graduate students
- Immediately engages students using simple, concrete examples
- Contains numerous exercises with solutions
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Reviews & endorsements
'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

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Product details
- Date Published: April 2011
- format: Hardback
- isbn: 9780521474238
- length: 572 pages
- dimensions: 229 x 152 x 37 mm
- weight: 1.01kg
- contains: 180 exercises
- availability: 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.
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Authors
Dorian Goldfeld, Columbia University, New York
Dorian Goldfeld is a Professor in the Department of Mathematics at Columbia University, New York.
Joseph Hundley, State University of New York, Buffalo
Joseph Hundley is an Assistant Professor in the Department of Mathematics at Southern Illinois University, Carbondale.