Automorphic Representations and L-Functions for the General Linear Group
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- Dorian Goldfeld, Columbia University, New York
- Joseph Hundley, Southern Illinois University, Carbondale
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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, this book will motivate students and researchers to begin working in this fertile field of research.Read more
- Presents clear, detailed proofs suitable for graduate students
- Immediately engages students using simple, concrete examples
- Contains numerous exercises with solutions
Reviews & endorsements
"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
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- Date Published: May 2011
- format: Adobe eBook Reader
- isbn: 9781139066266
- contains: 55 exercises
- availability: Adobe Reader ebooks available from eBooks.com
Table of Contents
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
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