A Note on p-adic Linear Differential Equations Original Research Article

Let image be the algebraic closure of image in the field imagep of p-adic numbers. In an earlier paper (1997, in Lecture Notes in Pure and Appl. Math., Vol. 192, pp. 49–59, Dekker, New York), we showed that if a function f(x) meromorphic in all imagep is a solution of a homogeneous linear differential equation (E) with coefficients in image(x), then fset membership, variantimagep(x). Here we show that this conclusion is false in the case where (E) is with coefficients not in image(x).