Liouvillian solutions of linear difference-differential equations

摘要

For a field k with an automorphism σ and a derivation δ we introduce the notion of Liouvillian solutions of linear difference-differential systems {σ(Y) - AY, δ(Y) = BY} 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 difference-differential systems of prime order have Liouvillian solutions.