Resumen de Liouvillian solutions of linear difference�differential equations

Ruyong Feng, Michael F. Singer, Min Wu

• For a field k with an automorphism  and a derivation , we introduce the notion of Liouvillian solutions of linear difference differential systems f.Y/ D AY; .Y/ D BYg over k and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the forthcoming paper, we will propose an algorithm for deciding if linear differencedifferential systems of prime order have Liouvillian solutions.