Modular Forms Spring 2022

Lecturer
Sarah Zerbes
Coordinator
Baptiste Depouilly | baptiste.depouilly@math.ethz.ch
Lectures
Tuesdays 10:00-12:00 HG G3
Fridays 10:00-11:00 HG G3
Course Catalogue
401-4118-22L Modular Forms
Abstract
Modular forms are ubiquitous in number theory. This course aims to give an introduction to this beautiful theory, using methods from number theory, complex analysis and geometry.

Content

In this course you will learn about:

Recommended readings can be found in the Literature section below.

Recordings

Recordings of the lecture are available here. Note that you will have to log in with your ETH credentials to access the videos.

Lecture notes

The full lecture notes can be found here. Under, you can find the notes corresponding to each lecture and some additional material/references.

Week Date Notes Resources
1 22.02 Lecture 1
25.02 Lecture 2 M. C. Escher's lizards, Fundamental domain for the action of the modular group
2 01.03 Lecture 3
04.03 Lecture 4
3 08.03 Lecture 5
11.03 Lecture 6
4 15.03 Lecture 7
18.03 Lecture 8 Reference 1 section 1.2.
5 22.03 Lecture 9
25.03 Lecture 10
6 29.03 Lecture 11
01.04 Lecture 12 For exact computations of \(\dim(M_k)\) see Reference 1, chapter 3.
7 05.04 Lecture 13
08.04 Lecture 14 Reference 1 section 5.1.
8 12.04 Lecture 15
15.04 No lecture
9 26.04 Lecture 16 Exercise class: Theta series and modular forms
29.04 Lecture 17
10 03.05 Lecture 18
06.05 Lecture 19
11 10.05 Lecture 20 Reference 1 section 5.4.
13.05 Lecture 21 Reference 1 section 5.5.
12 17.05 Lectures 22 & 23 Reference 1 section 5.6.
20.05
13 24.05 Lectures 24 & 25
27.05
14 31.05 Lectures 26 & 27 Lecture notes on modular curves
03.06

Exercises

The new problem sheets will be posted here every Friday. You are strongly encouraged to try to solve them and to prepare questions before the following Tuesday. You are also invited to hand in the problems that you want to receive feedback on.

Exercise sheet Hand-in by Solutions
Problem Sheet 1 04.03 Solutions 1
Problem Sheet 2 11.03 Solutions 2
Problem Sheet 3 18.03 Solutions 3
Problem Sheet 4 25.03 Solutions 4
Problem Sheet 5 01.04 Solutions 5
Problem Sheet 6 08.04 Solutions 6
Problem Sheet 7 15.04 Solutions 7
Problem Sheet 8 06.05 Solutions 8
Problem Sheet 9 13.05 Solutions 9
Problem Sheet 10 20.05 Solutions 10
Problem Sheet 11 27.05 Solutions 11

Forum

You can find the D-MATH forum for this course here.

Literature

  1. A First Course in Modular Forms by F. Diamond, J. Shurman
  2. Modular Forms by T. Miyake

Last updated: 03.06.2022