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401-4118-DRL 3 Credits DR D-MATH

Modular Forms

Lecturers & Examiners: Prof. Dr. Sarah Zerbes
Only 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 ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-02-05 16:07:26

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)

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture with exercise Modular Forms
  • Tue 10:15-12:00 (HG G 3)
  • Fri 10:15-11:00 (HG G 3)
3 h weekly

Offered In

  • Doctorate Mathematics (More Information at: )
    • Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
      • Graduate School (Official website of the Zurich Graduate School in Mathematics: In addition to the 401-....-DRL course units, adapted versions for doctoral students of the following course units: 263-4400-00L Advanced Graph Algorithms and Optimization 401-3902-21L Network & Integer Optimization: From Theory to Application 401-3904-22L Convex Optimization 401-3629-00L Quantitative Risk Management 401-3652-00L Numerical Methods for Hyperbolic Partial Differential Equations 151-0530-00L Nonlinear Dynamics and Chaos II 227-0434-10L Mathematics of Information 401-4490-22L Topology Optimization of Engineering Systems ... (continued ))