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401-3110-21L 4 Credits BSC , MSC D-MATH

Student Seminar in Number Theory: Modular Forms

Lecturers & Examiners: Dr. Markus Schwagenscheidt
Number of participants limited to 26.
VVZ CR n/a

Last Updated: 2026-02-05 15:54:09

Abstract

Seminar on the basic theory of classical elliptic modular forms

Objective

In the seminar we will learn about the basic theory of classical elliptic modular forms. We start with the action of the modular group on the complex upper half-plane by Moebius transformations and describe its fundamental domain. As first examples of modular forms, we will investigate Eisenstein series, Ramanujan's Delta function, the Dedekind eta function, and the modular j-invariant. We will show that the space of modular forms of a fixed weight is finite dimensional, and determine its dimension. We will also study Hecke operators and the Petersson inner product on spaces of modular forms, and the L-functions associated with modular forms. Towards the end of the seminar we will discuss some more advanced topics, such as differential operators and quasimodular forms, the CM values of the j-function, and the periods of modular forms.

Resources

Lecture Notes

Link

Literature

Cohen, Strömberg: Modular Forms: A Classical Approach Diamond, Shurman: A first course in modular forms Koblitz: Introduction to elliptic curves and modular forms Koecher, Krieg: Elliptische Funktionen und Modulformen Lang: Introduction to modular forms Miyake: Modular forms Serre: A course in arithmetic Zagier: The 1-2-3 of modular forms Lecture notes on modular forms, available online: Link

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup Start
04.01.2021
Signup End
19.02.2021
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Student Seminar in Number Theory: Modular Forms
Die genauen Unterrichtszeiten von ONLINE - Veranstaltungen werden von den Dozierenden kommuniziert.
  • Fri 12:00-14:00 (ON LI NE)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and a few minutes later choose an alternative seminar. IMPORTANT: Do not waitlist yourself for more than two seminars!)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and a few minutes later choose an alternative seminar. IMPORTANT: Do not waitlist yourself for more than two seminars!)