Lectures:

Course Description:

This is a two-semester course for introduction to automorphic representations and L-functions.

Automorphic Representations and Automorphic L-functions form the core of the modern theory of
automorphic forms, especially, in the Langlands Program, which unifies the arithmetic geometry, number
theory and harmonic analysis in terms of L-functions via various types of Langlands functoriality.

In this course, we mainly discuss the theory for GL(n), the general linear group. The topics are:

1) Basic theory of automorphic representations of GL(n)
2) Automorphic L-functions for GL(n)
3) Converse theorem for GL(n) and the Langlands functoriality
4) The residual spectrum for GL(n) (Spring 2009)
5) More advanced topics (Spring 2009)

The lectures may follow a few books or research papers. However, the following two books provides basic facts and
guidelines for Topics 1-3 above:

1) Traces of Hecke Operators by A. Knightly and C. Li, Math. Surveys and Monographs 133, 2006, AMS
2) Lectures on Automorphic L-functions by J. Cogdell, H. Kim, and M. Murty, Fields Inst. Monographs 20, 2004, AMS
3) Automorphic Forms and Representations By D. Bump, cambridge Studies in Advanced Math. 55, 1998
4) Algebraic Groups And Number Theory by V. Platonov With A. Rapinchuk, Pure and Applied Math. 139, A Wiley-Interscience Series of Texts, Monographs and Tracts, 1993

Up to a certain point, guest speakers may be invited to lecture on recent progress of the theory.

Homework and Exams:

Homework Problems will be assigned, but no exams are required. Students may give reports to the class.