Cover......Page 1
Title page......Page 4
Contents......Page 6
Preface......Page 12
Lectures on ��-functions, converse theorems, and functoriality for ����_{��}, by James W. Cogdell......Page 14
Preface......Page 16
Lecture 1. Modular forms and their ��-functions......Page 18
Lecture 2. Automorphic forms......Page 26
Lecture 3. Automorphic representations......Page 34
Lecture 4. Fourier expansions and multiplicity one theorems......Page 42
Lecture 5. Eulerian integral representations......Page 50
Lecture 6. Local ��-functions: The non-Archimedean case......Page 58
Lecture 7. The unramified calculation......Page 64
Lecture 8. Local ��-functions: The Archimedean case......Page 72
Lecture 9. Global ��-functions......Page 78
Lecture 10. Converse theorems......Page 86
Lecture 11. Functoriality......Page 94
Lecture 12. Functoriality for the classical groups......Page 100
Lecture 13. Functoriality for the classical groups, II......Page 104
Automorphic ��-functions, by Henry H. Kim......Page 110
Introduction......Page 112
Chevalley groups and their properties......Page 114
Cuspidal representations......Page 126
��-groups and automorphic ��-functions......Page 128
Induced representations......Page 132
Eisenstein series and constant terms......Page 142
��-functions in the constant terms......Page 150
Meromorphic continuation of ��-functions......Page 158
Generic representations and their Whittaker models......Page 160
Local coefficients and non-constant terms......Page 166
Local Langlands correspondence......Page 174
Local ��-functions and functional equations......Page 178
Normalization of intertwining operators......Page 184
Holomorphy and bounded in vertical strips......Page 190
Langlands functoriality conjecture......Page 194
Converse theorem of Cogdell and Piatetski-Shapiro......Page 196
Functoriality of the symmetric cube......Page 200
Functoriality of the symmetric fourth......Page 206
Bibliography......Page 212
Applications of symmetric power ��-functions, by M. Ram Murty......Page 216
Preface......Page 218
Lecture 1. The Sato-Tate conjecture......Page 220
Lecture 2. Maass wave forms......Page 226
Lecture 3. The Rankin-Selberg method......Page 232
Lecture 4. Oscillations of Fourier coefficients of cusp forms......Page 240
Lecture 5. Poincaré series......Page 250
Lecture 6. Kloosterman sums and Selberg’s conjecture......Page 256
Lecture 7. Refined estimates for Fourier coefficients of cusp forms......Page 260
Lecture 8. Twisting and averaging of ��-series......Page 266
Lecture 9. The Kim-Sarnak theorem......Page 270
Lecture 10. Introduction to Artin ��-functions......Page 278
Lecture 11. Zeros and poles of Artin ��-functions......Page 284
Lecture 12. The Langlands-Tunnell theorem......Page 288
Bibliography......Page 294
Back Cover......Page 298