Automorphic Representations and L-functions for the General Linear Group: Volume 1 (Hardcover)

Dorian Goldfeld

ISBN 10: 052147423X / ISBN 13: 9780521474238

Editore: Cambridge University Press, Cambridge, 2011

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Hardcover. 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. This modern approach to the theory of automorphic representations keeps definitions to a minimum, focusing instead on providing concrete examples and detailed proofs of the key theorems. This book is the perfect introduction for students at the advanced undergraduate level and beyond, and for researchers new to the field. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780521474238

Dati bibliografici

Titolo: Automorphic Representations and L-functions ...

Casa editrice: Cambridge University Press, Cambridge

Data di pubblicazione: 2011

Legatura: Hardcover

Condizione: new

Descrizione articolo

Riassunto:

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.

Recensione:

'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