Math 6110 (Topics in automorphic forms)
Fall 2022, UNT

Lecture: GAB 461, TR 2:00-3:20pm

Instructor: Professor Olav Richter

• Office: GAB 412
• Office hours: TR 12:30-1:50pm, TR 3:30-4:00pm, and by appointment
• email: richter@unt.edu

Course Description: Math 6110 is intended for all graduate students in mathematics. We will cover selected topics in automorphic forms. A solid background in complex analysis is required and some basic knowledge in group theory will be helpful. Topics include: The modular group and its subgroups, elliptic functions, modular forms (including the discussion of various examples), and Hecke-Petersson theory.

Textbook: You do not have to buy a textbook for this class, since we will not follow a particular textbook very closely. A large portion of the material that we will cover can be found for example in the following books:

• Title: Modular Functions and Dirichlet Series in Number Theory
• Author: Tom M. Apostol
• Publisher: Springer

• Title: Elliptic modular forms and their applications in The 1-2-3 of Modular Forms
• Author: Don Zagier
• Publisher: Springer

There is also an excellent book by Koecher and Krieg that contains most of the material that we will cover. It has the slight (!) disadvantage that it is written in German:

• Title: Elliptische Funktionen und Modulfunktionen
• Author: Max Koecher and Aloys Krieg
• Publisher: Springer

Homework & Grading Policy: There will be a few homework assignments this semester, and your final grade will be based on these homework assignments. Homework assignments will be posted on canvas and you will upload your solutions on canvas.