401-4118-DRL  Modular Forms

SemesterFrühjahrssemester 2022
DozierendeS. Zerbes
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch
KommentarOnly for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“.


KurzbeschreibungModular 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.
LernzielThe aim of this course is to give an introduction to the theory of modular forms. In particular, we will cover the following topics:
- modular group and fundamental domains
- modular forms as functions on the complex upper half plane
- the valence formula
- Eisenstein series
- Hecke operators
- Petersson inner product
- L-functions of modular forms
- a geometric view of modular forms
Inhalt- modular group and fundamental domains
- modular forms as functions on the complex upper half plane
- the valence formula
- Eisenstein series
- Hecke operators
- Petersson inner product
- L-functions of modular forms
- a geometric view of modular forms
SkriptThe lecture notes will be uploaded to the website after each lecture. Also, the lectures will be recorded.
Literatur- A first course in Modular Forms, F. Diamond, J. Shurman
- Modular Forms, T. Miyake