First lecture: |
Lectures will be posted here regularly in the form of videos and scanned lecture notes. |

In this lecture we will focus on proving identities involving modular functions and modular forms. The course has an algorithmic flavour and is adapted for people who are interested in algorithms and programming. Also if time allows we will model sums using difference fields. This can be seen as a modest introduction to Symbolic Summmation methods used and developed by Carsten Schneider. Topics covered in the course are

- Sturm's theorem for modular forms
- Dedekind Eta function
- Weierstrass gap theorem
- Symbolic summation using difference fields
- Newman's theorem on Eta quotients

The material does not follow any particular book, however the notions used in the course are standard and can be googled or searched in Wikipedia.

Requirements: Basic knowledge from analysis and linear algebra.

Exercise instructor: Nicolas Smoot (nsmoot@risc.jku.at)

The exercises will be stated in the lectures in form of "homeworks" and will be sent by email to Nicolas Smoot.