Representation theory and automorphic forms / Toshiyuki Kobayashi, Wilfrid Schmid and Jae-Hyun Yang, Editors.

Format:

Book

Contributor:

Kobayashi, Toshiyuki, 1962-

Schmid, Wilfried, 1943-

Yang, J.

Series:

Progress in mathematics (Boston, Mass.) ; vol. 255.

Progress in mathematics ; v. 255

Language:

English

Subjects (All):

Automorphic forms.

Representations of groups.

Physical Description:

viii, 210 pages : illustrations ; 24 cm.

Place of Publication:

Boston, Mass. : Birkhäuser, 2008.

Summary:

This volume addresses the interplay between representation theory and automorphic forms. The invited papers, written by leading mathematicians, track recent progress in the ever expanding fields of representation theory and automorphic forms, and their association with number theory and differential geometry.

Representation theory relates to number theory through the Langlands program, which conjecturally connects algebraic extensions of number fields to automorphic representations and L-functions. These are the subject of several of the papers. Multiplicity-free representations constitute another subject, which is approached geometrically via the notion of visible group actions on complex manifolds. Both graduate students and researchers will find inspiration in this volume.

Contents:

1 Irreducibility and Cuspidality / Dinakar Ramakrishnan 1

2 The first step in the proof 15

3 The second step in the proof 16

4 Galois representations attached to regular, selfdual cusp forms on GL(4) 18

5 Two useful lemmas on cusp forms on GL(4) 20

6 Finale 21

2 On Liftings of Holomorphic Modular Forms / Tamotsu Ikeda 29

2 Fourier coefficients of the Eisenstein series 30

3 Kohnen plus space 32

4 Lifting of cusp forms 33

5 Outline of the proof 34

6 Relation to the Saito-Kurokawa lifts 35

7 Hermitian modular forms and hermitian Eisensetein series 37

8 The case m = 2n + 1 39

9 The case m = 2n 40

10 L-functions 40

11 The case m = 2 41

3 Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs / Toshiyuki Kobayashi 45

2 Main machinery from complex geometry 56

3 Proof of Theorem A 61

4 Proof of Theorem C 68

5 Uniformly bounded multiplicities - Proof of Theorems B and D 70

6 Counterexamples 77

7 Finite-dimensional cases - Proof of Theorems E and F 83

8 Generalization of the Hua-Kostant-Schmid formula 89

9 Appendix: Associated bundles on Hermitian symmetric spaces 103

4 The Rankin-Selberg Method for Automorphic Distributions / Stephen D. Miller, Wilfried Schmid 111

2 Standard L-functions for SL(2) 115

3 Pairings of automorphic distributions 121

4 The Rankin-Selberg L-function for GL(2) 128

5 Exterior Square on GL(4) 137

5 Langlands Functoriality Conjecture and Number Theory / Freydoon Shahidi 151

2 Modular forms, Galois representations and Artin L-functions 152

3 Lattice point problems and the Selberg conjecture 156

4 Ramanujan conjecture for Maass forms 158

5 Sato-Tate conjecture 159

6 Functoriality for symmetric powers 161

7 Functoriality for classical groups 163

8 Ramanujan conjecture for classical groups 164

6 Discriminant of Certain K3 Surfaces / Ken-Ichi Yoshikawa 175

1 Introduction - Discriminant of elliptic curves 175

2 K3 surfaces with involution and their moduli spaces 178

3 Automorphic forms on the moduli space 180

4 Equivariant analytic torsion and 2-elementary K3 surfaces 182

5 The Borcherds products 184

6 Borcherds products for odd unimodular lattices 186

7 K3 surfaces of Matsumoto-Sasaki-Yoshida 188

8 Discriminant of quartic surfaces 200.

Notes:

Includes bibliographical references and index.

ISBN:

0817645055

9780817645052

OCLC:

77012762