|Modular Forms, Maass Forms and Automorphic Forms on GL(2); An Introduction|
|Time：||Tue/Thu 10:10-12:00, 07-02~07-18|
|Instructor：||Freydoon Shahidi [Purdue University]|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building|
In these lectures we discuss the theory of classical modular forms on upper half plane. We briefly explain the geometry involved and sketch how the dimension of their spaces can be calculated. Finally, we sketch the standard proof of functional equations satisfied by them. We then turn to the theory of Maass forms, discussing their basic properties and explain the so called Ramanujan conjecture for them. We then relate these objects to automorphic forms on GL(2). Time permitting, we will discuss how the theory of automorphic forms on GL(2) can lead to progress towards the Ramanujan conjecture and other problems in classical theory.
G. Shimura, Introduction to arithmetic theory of automorphic functions.
H. Iwaniec: Introduction to the Spectral theory of Automorphic forms.
S. Gelbart: Automorphic forms on adele groups.
D. Bump: Automorphic forms and representations.