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401-3112-23L 8 Credits BSC , MSC D-MATH
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Number Theory II: Introduction to Modular Forms

Lecturers & Examiners: Prof. Dr. Özlem Imamoglu
Be aware that there is a big overlap with former course units on modular forms, in particular with 401-4118-22L taught in the Spring Semester 2022 as an elective course. Only one of the two course units may be recognised for credits. More precisely, it is also not allowed to have recognised one course unit for the Bachelor's and the other course unit for the Master's degree.
VVZ CR n/a

Last Updated: 2026-02-05 16:22:17

Abstract

This is a introductory course on automorphic forms covering its basic properties with emphasis on connections with number theory.

Objective

The aim of the course is to cover the classical theory of modular forms

Content

Basic definitions and properties of SL(2,Z), its subgroups and modular forms for SL(2,Z). Eisenstein and Poincare series. L-functions of modular forms. Hecke operators. Theta functions. Possibly Maass forms. Possibly automorphic forms for more general groups.

Resources

Literature

J.P. Serre, A Course in Arithmetic; N. Koblitz, Introduction to Elliptic Curves and Modular Forms; D. Zagier, The 1-2-3 of Modular Forms; H. Iwaniec, Topics in Classical Automorphic Forms.

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture with exercise Number Theory II: Introduction to Modular Forms
exercises Fri 10-12 bi-weekly in two classes.
  • Tue 10:15-12:00 (HG E 22)
  • Fri 10:15-12:00 (HG F 5)
  • Fri 10:15-12:00 (ML J 37.1)
4 h weekly

Offered In