T. Kobayashi, W. Schmid, and J.-H. Yang (eds.),
Representation theory and automorphic forms, Progr. Math. 255, Birkhäuser, 2007. ISBN 0817645055.

Representation Theory and Automorphic Forms

Table of contents
1 Irreducibility and Cuspidality  Dinakar Ramakrishnan1
  1 Preliminaries5
  2 The first step in the proof15
  3 The second step in the proof16
  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 Finale21
2 On Liftings of Holomorphic Modular Forms  Tamotsu Ikeda29
  1 Basic facts29
  2 Fourier coefficients of the Eisenstein series30
  3 Kohnen plus space32
  4 Lifting of cusp forms33
  5 Outline of the proof34
  6 Relation to the Saito-Kurokawa lifts35
  7 Hermitian modular forms and hermitian Eisensetein series37
  8 The case m = 2n + 139
  9 The case m = 2n40
  10 L-functions40
  11 The case m = 241
3 Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs  Toshiyuki Kobayashi45
  1 Introduction and statement of main results45
  2 Mainmachinery fromcomplex geometry56
  3 Proof of Theorem A61
  4 Proof of Theorem C68
  5 Uniformly bounded multiplicities — Proof of Theorems B and D70
  6 Counterexamples77
  7 Finite-dimensional cases — Proof of Theorems E and F83
  8 Generalization of the Hua-Kostant-Schmid formula88
  9 Appendix: Associated bundles on Hermitian symmetric spaces103
4 The Rankin-Selberg Method for Automorphic Distributions  Stephen D. Miller and Wilfried Schmid111
  1 Introduction111
  2 Standard L-functions for SL(2)115
  3 Pairings of automorphic distributions121
  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 Shahidi151
  1 Introduction151
  2 Modular forms, Galois representations and Artin L-functions152
  3 Lattice point problems and the Selberg conjecture156
  4 Ramanujan conjecture for Maass forms158
  5 Sato-Tate conjecture159
  6 Functoriality for symmetric powers161
  7 Functoriality for classical groups163
  8 Ramanujan conjecture for classical groups164
  9 The method166
6 Discriminant of Certain K3 Surfaces  Ken-Ichi Yoshikawa175
  1 Introduction — Discriminant of elliptic curves175
  2 K3 surfaces with involution and their moduli spaces178
  3 Automorphic forms on the moduli space180
  4 Equivariant analytic torsion and 2-elementary K3 surfaces182
  5 The Borcherds products184
  6 Borcherds products for odd unimodular lattices186
  7 K3 surfaces of Matsumoto-Sasaki-Yoshida188
  8 Discriminant of quartic surfaces200
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