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Last Updated: 2026-02-05 16:06:49
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.
Objective
The 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
Content
- 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
Resources
Lecture Notes
The lecture notes will be uploaded to the website after each lecture. Also, the lectures will be recorded.
Literature
- A first course in Modular Forms, F. Diamond, J. Shurman - Modular Forms, T. Miyake
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Modular Forms |
|
3 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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