Special Functions and Symbolic Summation II

Lecturers: Dr. Nicolas Smoot, Dr. Silviu Radu

Lecture no.: 326.00D

ECTS: 1.5, hours: 1

Schedule: see KUSSS

Abstract:

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

A major emphasis of the lecture is to present the basic notions, to develop the basic ideas of the underlying algorithms and to put computer algebra into action for concrete examples.