Automorphic forms and applications / ed. by P.Sarnak, F.Shahidi. - Providence: American Mathematical Society: Institute for Advanced Study, 2007. - xiv, 427 p.: ill. (some col.), port. - (IAS/Park City mathematics series; Vol.12). - Bibliogr.: p.425-427. - ISBN 978-0-8218-2873-1; ISSN 1079-5634  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Preface ...................................................... xiii Introduction .................................................... 1 Armand Borel, Automorphic Forms on Reductive Groups ............. 5 Introduction .................................................... 7 1. Notation .................................................... 7 2. Notion of automorphic form .................................. 8 3. First properties of automorphic forms ....................... 9 4. Reductive groups (review) .................................. 12 5. Arithmetic subgroups. Reduction theory ..................... 19 6. Constant terms. The basic estimate ......................... 24 7. Finite dimensionality of А(Г, J, ξ) ........................ 28 8. Convolution operators on cuspidal functions ................ 29 9. Automorphic forms and the regular representation on Г\G .... 30 10. A decomposition of the space of automorphic forms .......... 32 11. Some estimates of growth functions ......................... 33 12. Eisenstein series .......................................... 35 Bibliography ................................................... 39 L. Clozel, Spectral Theory of Automorphic Forms ................ 41 Foreword ....................................................... 43 Lecture 1. Mostly SL(2) ........................................ 47 Lecture 2. The spectral decomposition of L2(G()\G()): Arthur's conjectures ................................ 57 Lecture 3. Known bounds for the cuspidal spectrum and the Burger-Sarnak method ............................ 65 Lecture 4. Applications: control of the spectrum ............... 79 Appendix: All reductive adelic groups are tame ................. 87 Bibliography ................................................... 89 James W. Cogdell, L-functions and Converse Theorems for GLn .... 95 Introduction ................................................... 97 Lecture 1. Fourier expansions and multiplicity one ............ 101 Lecture 2. Eulerian integrals for GLn ......................... 111 Lecture 3. Local L-functions .................................. 123 Lecture 4. Global L-functions ................................. 137 Lecture 5. Converse theorems .................................. 147 Lecture 6. Converse theorems and functoriality ................ 161 Bibliography .................................................. 173 Philippe Michel, Analytic Number Theory and Families of Automorphic L-functions ....................................... 179 Foreword ...................................................... 181 Lecture 1. Analytic properties of individual L-functions ...... 187 Lecture 2. A review of classical automorphic forms ............ 211 Lecture 3. Large sieve inequalities ........................... 223 Lecture 4. The subconvexity problem ........................... 241 Lecture 5. Some applications of subconvexity .................. 267 Bibliography .................................................. 285 Freydoon Shahidi, Langlands-Shahidi Method .................... 297 Foreword ...................................................... 299 Lecture 1. Basic concepts ..................................... 301 Lecture 2. Eisenstein series and L-functions .................. 307 Lecture 3. Functional equations and multiplicativity .......... 315 Lecture 4. Holomorphy and boundedness; applications ........... 321 Bibliography .................................................. 327 Audrey Terras, Arithmetical Quantum Chaos ..................... 331 Abstract ...................................................... 333 Lecture 1. Finite models ...................................... 335 Lecture 2. Three symmetric spaces ............................. 355 Bibliography .................................................. 371 David A. Vogan, Jr, Isolated Unitary Representations .......... 377 Bibliography .................................................. 397 Wen-Ching Winnie Li, Ramanujan Graphs and Ramanujan Hypergraphs ................................................... 399 Introduction .................................................. 401 Lecture 1. Ramanujan graphs and connections with number theory ............................................. 403 Lecture 2. Ramanujan hypergraphs .............................. 415 Bibliography .................................................. 425