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.
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