The Conference on L-functions: Fukuoka, Japan, 18-23 February 2006

Contents......Page 10
Preface......Page 6
List of Participants......Page 8
Quantum Maass Forms......Page 12
1 Quantum Maass forms associated to Maass cusp forms and Eisenstein series......Page 13
2 Quantum Maass forms associated to invariant eigenfunctions......Page 20
References......Page 26
Introduction......Page 28
1 Lecture 1: Galois deformation and L-invariant......Page 35
2 Lecture 2: Elliptic curves with multiplicative reduction......Page 42
3 Lecture 3: L-invariants of CM fields......Page 48
4 Appendix: Differential and adjoint square Selmer group......Page 55
References......Page 61
Siegel Modular Forms of Weight Three and Conjectural Correspondence of Shimura Type and Langlands Type......Page 66
1 Definition of Siegel modular forms......Page 67
2 Conjectures on dimensions of weight 3......Page 68
3 Conjecture on Eichler type correspondence......Page 71
4 Geometric interpretation......Page 75
5 Conjecture on Shimura type correspondence......Page 76
References......Page 78
0 Introduction......Page 82
1 An arithmetic formula for Fourier coefficients......Page 84
2 Applications to convolutions......Page 89
References......Page 96
On an Extension of the Derivation Relation for Multiple Zeta Values......Page 100
References......Page 105
1 Symmetric fourth......Page 106
2 Symmetric mth powers......Page 109
3 First occurences of poles of symmetric power L-functions......Page 114
4 Descent to cuspidal representations on classical groups......Page 116
5 Remark on the images of functorial lift......Page 119
References......Page 122
0 Introduction......Page 126
1 Zeta functions of root systems......Page 129
2 Structural background of functional relations......Page 132
3 Functional relations for S3(s; A3)......Page 136
References......Page 149
1 Automorphic forms......Page 152
2 Sum formulas......Page 155
3 The inversion problem......Page 158
4 Proof (1)......Page 160
5 Proof (2)......Page 165
6 Concluding remarks......Page 170
References......Page 172
1 The Selberg class......Page 176
2 The Lindelof class......Page 178
References......Page 184
0 Introduction......Page 186
1 The idea of the proof......Page 188
2 The frame of the proof......Page 190
3 Proof of Theorem 1......Page 193
4 Proof of Lemma 1......Page 203
5 Proof of Lemma 5......Page 206
References......Page 209
0 Introduction......Page 212
1 Setting the stage......Page 216
2 Elliptic curves associated with J2(n)......Page 218
3 Geometric interpretation of the differential equation for W2(T)......Page 220
4 Modular properties......Page 222
5 Closing remarks......Page 225
References......Page 228
A Geometric Approach to L-Functions......Page 230
1 High Rank Zetas for Number Fields......Page 234
2 Non-Abelian L-Functions......Page 265
3 Geometric and Analytic Truncations......Page 275
4 Rankin-Selberg & Zagier Method......Page 307
5 High Rank Zetas and Eisenstein Series......Page 326
6 Stability and Distance to Cusps......Page 332
7 Explicit Formulas for Rank Two Zetas......Page 342
8 Zeros of Rank Two Zetas......Page 347
9 A Rank Three Zeta and Its Zeros......Page 353
REFERENCES......Page 376