Departmental Colloquium
Michael Singer
North Carolina State University
Differential Groups and the Gamma Function
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.
Friday February 13, 2009 at 3:00 PM in SEO 636