Representation Theory and Automorphic Forms, Vol. 255 Book

Preface     vii
Irreducibility and Cuspidality   Dinakar Ramakrishnan     1
Preliminaries     5
The first step in the proof     15
The second step in the proof     16
Galois representations attached to regular, selfdual cusp forms on GL(4)     18
Two useful lemmas on cusp forms on GL(4)     20
Finale     21
References     25
On Liftings of Holomorphic Modular Forms   Tamotsu Ikeda     29
Basic facts     29
Fourier coefficients of the Eisenstein series     30
Kohnen plus space     32
Lifting of cusp forms     33
Outline of the proof     34
Relation to the Saito-Kurokawa lifts     35
Hermitian modular forms and hermitian Eisensetein series     37
The case m = 2n + 1     39
The case m = 2n     40
L-functions     40
The case m = 2     41
References     42
Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs   Toshiyuki Kobayashi     45
Introduction and statement of main results     45
Main machinery from complexgeometry     56
Proof of Theorem A     61
Proof of Theorem C     68
Uniformly bounded multiplicities - Proof of Theorems B and D     70
Counterexamples     77
Finite-dimensional cases - Proof of Theorems E and F     83
Generalization of the Hua-Kostant-Schmid formula     89
Appendix: Associated bundles on Hermitian symmetric spaces     103
References     105
The Rankin-Selberg Method for Automorphic Distributions   Stephen D. Miller   Wilfried Schmid     111
Introduction     111
Standard L-functions for SL(2)     115
Pairings of automorphic distributions     121
The Rankin-Selberg L-function for GL(2)     128
Exterior Square on GL(4)     137
References     149
Langlands Functoriality Conjecture and Number Theory   Freydoon Shahidi     151
Introduction     151
Modular forms, Galois representations and Artin L-functions     152
Lattice point problems and the Selberg conjecture     156
Ramanujan conjecture for Maass forms     158
Sato-Tate conjecture     159
Functoriality for symmetric powers     161
Functoriality for classical groups     163
Ramanujan conjecture for classical groups     164
The method     166
References     169
Discriminant of Certain K3 Surfaces   Ken-Ichi Yoshikawa     175
Introduction - Discriminant of elliptic curves     175
K3 surfaces with involution and their moduli spaces     178
Automorphic forms on the moduli space     180
Equivariant analytic torsion and 2-elementary K3 surfaces     182
The Borcherds products     184
Borcherds products for odd unimodular lattices     186
K3 surfaces of Matsumoto-Sasaki-Yoshida     188
Discriminant of quartic surfaces     200
References     209