Automorphic Forms and Representations,9780521658188

Automorphic Forms and Representations

by
ISBN13: 9780521658188
ISBN10: 0521658187
Format: Paperback
Pub. Date: 1999-01-01
Publisher(s): Cambridge Univ Pr
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Summary

This book covers both the classical and representation theoretic views of automorphic forms in a style that is accessible to graduate students entering the field. The treatment is based on complete proofs, which reveal the uniqueness principles underlying the basic constructions. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin-Selberg method and the triple L-function, and examines this subject matter from many different and complementary viewpoints. Researchers as well as students in algebra and number theory will find this a valuable guide to a notoriously difficult subject.

Table of Contents

Preface ix(2)
Advice to the Reader xi(3)
Prerequisities xiv(1)
Notations xv
1 Modular Forms
1(126)
1.1 Dirichlet L-Functions
3(14)
1.2 The Modular Group
17(9)
1.3 Modular Forms for SL(2, Z)
26(15)
1.4 Hecke Operators
41(13)
1.5 Twisting
54(11)
1.6 The Rankin-Selberg Method
65(11)
1.7 Hecke Characters and Hilbert Modular Forms
76(14)
1.8 Artin L-Functions and Langlands Functoriality
90(13)
1.9 Maass Forms
103(16)
1.10 Base Change
119(8)
2 Automorphic Forms and Representations of GL(2, R)
127(125)
2.1 Maass Forms and the Spectral Problem
128(17)
2.2 Basic Lie Theory
145(20)
2.3 Discreteness of the Spectrum
165(21)
2.4 Basic Representation Theory
186(17)
2.5 Irreducible (g, K)-Modules for GL(2, R)
203(19)
2.6 Unitaricity and Intertwining Integrals
222(19)
2.7 Representations and the Spectral Problem
241(2)
2.8 Whittaker Models
243(3)
2.9 A Theorem of Harish-Chandra
246(6)
3 Automorphic Representations
252(145)
3.1 Tate's Thesis
254(24)
3.2 Classical Automorphic Forms and Representations
278(13)
3.3 Automorphic Representations of GL(n)
291(16)
3.4 The Tensor Product Theorem
307(14)
3.5 Whittaker Models and Automorphic Forms
321(20)
3.6 Adelization of Classical Automorphic Forms
341(5)
3.7 Eisenstein Series and Intertwining Integrals
346(22)
3.8 The Rankin-Selberg Method
368(7)
3.9 The Global Langlands Conjectures
375(10)
3.10 The Triple Convolution
385(12)
4 Representations of GL(2) Over a p-adic Field
397(161)
4.1 GL(2) Over a Finite Field
398(26)
4.2 Smooth and Admissible Representations
424(12)
4.3 Distributions and Sheaves
436(16)
4.4 Whittaker Models and the Jacquet Functor
452(17)
4.5 The Principal Series Representations
469(21)
4.6 Spherical Representations
490(21)
4.7 Local Functional Equations
511(12)
4.8 Supercuspidals and the Weil Representation
523(26)
4.9 The Local Langlands Correspondence
549(9)
Bibliography 558(10)
Index 568

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