Michael Singer : Differential Groups and the Gamma Function

Posted by , part of the Departmental Colloquium.

At

Feb. 13, 2009, 3 p.m.

In

SEO 636

Abstract

I will develop a Galois theory of linear difference equations where the Galois group are linear differential groups that is, groups of matrices whose entries satisfy a fixed set of polynomial differential equations. These groups measure the differential dependence among solutions of linear difference equations. I will show how this theory can be used to reprove Hoelder's Theorem that the Gamma function satisfies no differential polynomial equation as well as new results concerning differential dependence of solutions of higher order difference equations.