RATIONAL DECOMPOSITIONS OF p-ADIC MEROMORPHIC FUNCTIONS

Let K be a non archimedean algebraically closed field of characteristic π, complete for its ultrametric absolute value. In a recent paper by Escassut and Yang ([6]) polynomial decompositions P (f) = Q(g) for meromorphic functions f , g on K (resp. in a disk d(0, r−) ⊂ K) have been considered, and for a class of polynomials P , Q, estimates for the Nevanlinna function T (ρ, f) have been derived. In the present paper we consider as a generalization rational decompositions of meromorphic functions, i.e., we discuss properties of solutions f , g of the functional equation P (f) = Q(g), where P, Q are in K(x) and satisfy a certain condition (M). We infer that in the case, where f , g are analytic functions, the Second Nevanlinna Theorem yields an analogue result as in the mentioned paper [6]. However, if they are meromorphic, non trivial estimates for T (ρ, f) are more sophisticated.