Lecturer

Emmanuel Kowalski

Coordinator

Ana Marija Vego

Lectures

Wednesdays, 14 to 16 in HG E 1.1
Fridays, 10 to 12 in HG E 1.1.

Exercise classes will be held on average once every two weeks, usually during the Wednesday lecture. They will be announced in class and below.

The lectures should be automatically recorded; the video recordings will then be available on the ETH Video Portal.

Summary

The course is an introduction to modular forms and their applications in number theory.

Lecture notes

The course will be mostly based on the books of Serre and Iwaniec listed below. I will also post the scans of my handwritten lecture notes after each class with the summary of the content below.
For the basic background material in number theory, I will use mostly the lecture notes from the Number Theory I class of Fall 2024.

Exercises

The lecture will be accompanied by roughly biweekly exercise classes, usually during the Wednesday class. We will announce the precise dates in the lecture as well as here. You should submit your exercise sheets as a PDF upload to the SamUpTool.

Summary of the lectures

We will summarize here briefly the content of each lecture.

Literature

• Topics in classical automorphic forms, by H. Iwaniec (AMS 1994).
• A course in arithmetic, by J-P. Serre (Springer 1973).