Automorphic Representations and L-Functions for the General Linear Group: Volume 1

Nonfiction, Science & Nature, Mathematics, Number Theory
Cover of the book Automorphic Representations and L-Functions for the General Linear Group: Volume 1 by Dorian Goldfeld, Joseph Hundley, Cambridge University Press
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Author: Dorian Goldfeld, Joseph Hundley ISBN: 9781139635912
Publisher: Cambridge University Press Publication: April 21, 2011
Imprint: Cambridge University Press Language: English
Author: Dorian Goldfeld, Joseph Hundley
ISBN: 9781139635912
Publisher: Cambridge University Press
Publication: April 21, 2011
Imprint: Cambridge University Press
Language: English

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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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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