Automorphic Forms and Applications
About this Title
Peter Sarnak, Princeton University, Princeton, NJ and Freydoon Shahidi, Purdue University, West Lafayette, IN, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 2007; Volume 12
ISBNs: 978-0-8218-2873-1 (print); 978-1-4704-3911-8 (online)
MathSciNet review: MR2331351
MSC: Primary 00B25; Secondary 11-06, 22-06
The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as well as certain recent advances in the field.
The book starts with the lectures of Borel on the basic theory of automorphic forms, which lay the foundation for the lectures by Cogdell and Shahidi on converse theorems and the Langlands-Shahidi method, as well as those by Clozel and Li on the Ramanujan conjectures and graphs. The analytic theory of GL(2)-forms and $L$-functions are the subject of Michel's lectures, while Terras covers arithmetic quantum chaos. The volume also includes a chapter by Vogan on isolated unitary representations, which is related to the lectures by Clozel.
This volume is recommended for independent study or an advanced topics course. It is suitable for graduate students and researchers interested in automorphic forms and number theory.
Graduate students and research mathematicians interested in automorphic forms and number theory.
Table of Contents
- Automorphic Forms on Reductive Groups
- Spectral Theory of Automorphic Forms
- $L$-functions and Converse Theorems for $GL_n$
- Analytic Number Theory and Families of Automorphic $L$-functions
- Langlands-Shahidi Method
- Arithmetical Quantum Chaos
- Isolated Unitary Representations
- Ramanujan Graphs and Ramanujan Hypergraphs