Di erence Equations with Hypergeometric Coe cients

Let k be a diierence eld with automorphism. Let b be an element of k, and L be a linear ordinary diierence operator with coeecients in k. A classical problem in the theory of diierence equations is to compute all the solutions in k of the equation L(y) = b. If C denotes a constant eld and if k = C(n) and n = n + 1 or n = qn, there are known algorithms (see 2] for example). Manuel Bronstein presents here a generalization to monomial extensions of C(n) (see 6] for details and generalization).