DIS

Abstract

The aim of these two talks is to show how group theory can be used to derive properties of solutions of difference equations. The tools to do this are provided by Galois theories, which allow us to link groups to difference equations. I will give an elementary introduction to two such theories and show how they can be used to describe algebraic properties of sequences satisfying recurrence relations as well as differential properties of functions satisfying functional equations. For example, I will show how one can reprove and generalize Hoelder's result that the Gamma function satisfies no algebraic differential equation.