Liouvillian solutions of linear difference-differential equations

For a field k with an automorphism and a derivation , we introduce the notion of liouvillian solutions of linear difference-differential systems {(Y ) = AY, (Y ) = BY } over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x, t), (x) = x + 1, (t) = d dt and the size of the system is a prime. Contents

• Type: Journal
• Year: 2010
• Where: JSC
• Authors: Ruyong Feng, Michael F. Singer, Min Wu
• Keywords: Automorphism, Galois Group, JSC 2010, Liouvillian Solutions