Automorphic Representations and L-Functions for the General Linear Group : Volume 2 - Dorian Goldfeld

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Automorphic Representations and L-Functions for the General Linear Group

Volume 2

By: Dorian Goldfeld, Joseph Hundley

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Hardcover | 21 April 2011

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208 Pages

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22.86 x 15.24 x 1.27

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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.

Industry Reviews

"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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Contents for Volume 1	p. ix
Introduction	p. xv
Preface to the Exercises	p. xix
The classical theory of automorphic forms for GL (n, R)	p. 1
Iwasawa decomposition for GL(n, R)	p. 1
Congruence subgroups of SL(n, Z)	p. 2
Automorphic functions of arbitrary weight,level,and character	p. 3
Exercises for Chapter 12	p. 13
Automorphic forms and representations for GL(n, AQ)	p. 16
Cartan,Bruhat decompositions for GL(n, R)	p. 16
Iwasawa,Cartan, Bruhat decompositions for GL{n,Qp)	p. 17
Strong approximation for GL(n)	p. 22
Adelic lifts and automorphic forms for GL(n, AQ)	p. 24
The Fourier expansion of adelic automorphic forms	p. 31
Adelic automorphic representations for GL(n, AQ)	p. 36
Tensor product theorem for GL(n)	p. 41
Newforms for GL(n)	p. 43
Exercises for Chapter 13	p. 47
Theory of local representations for GL(n)	p. 52
Generalities on representations of GL(n, Qp)	p. 52
Generic representations of GL(n, Qp)	p. 56
Parabolic induction for GL(n, Qp)	p. 60
Supercuspidal representations of GL(n, Qp)	p. 66
The Bernstein-Zelevinsky classification for GL(n, Qp)	p. 70
Classification of smooth irreducible representations of GL(n, Qp) via the growth of matrix coefficients	p. 75
Unitary representations of GL(n, Qp)	p. 78
Generalities on (g,K8)-modules of GL(n, R)	p. 80
Generic representations of GL(n, R)	p. 85
Parabolic induction for GL(n, R)	p. 88
Classification of the unitary and the generic unitary representations of GL(n, Qp)	p. 100
Unramified representations of GL(n, Qp) and GL(n, R)	p. 102
Unitary duals and other duals	p. 105
The Ramanujan conjecture for GL(n, AQ)	p. 106
Exercises for Chapter 14	p. 106
The Godement-Jacquet L-function for GL(n, AQ)	p. 114
The Poisson summation formula for GL(n, AQ)	p. 114
The global zeta integral for GL(n, AQ)	p. 118
Factorization of the global zeta integral for GL(n, AQ)	p. 124
The local functional equation for GL(n, Qp)	p. 125
The L-function and local functional equation for the supercuspidal representations of GL(n, Qp)	p. 128
The local functional equation for tensor products	p. 128
The local zeta integral for a parabolically induced representation of GL(n, Qp)	p. 130
The local zeta integral for discrete series (square integrable) representations of GL(n, Qp)	p. 138
The local zeta integral for irreducible unitary generic representations of GL(n, R)	p. 143
Exercises for Chapter 15	p. 151
Solutions to Selected Exercises	p. 153
References	p. 169
Symbols Index	p. 175
Index	p. 179
Table of Contents provided by Ingram. All Rights Reserved.

Automorphic Representations and L-Functions for the General Linear Group

Volume 2

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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