2005/08/01 by Eberhard Mayerhofer
Mathematics · #math.CV #msc:30D05 #msc:30D35 #msc:11D88 #msc:11E95
published as Sci. Math. Jpn. 61 (2005), no. 1, 1--13 · 13 pages
arxiv created 2005/08/01 · arxiv updated 2009/12/01
Let K be a non archimedean algebraically closed field of characteristic pi complete for its ultrametric absolute value. In a recent paper by Escassut and Yang, polynomial decompositions P(f)=Q(g) for meromorphic functions f, g on K (resp. in a disk) have been considered, and for a class of polynomials P, Q, estimates for the Nevanlinna function T(r,f) have been derived. In the present paper we consider as a generalization rational decompositions of meromorphic functions. In the case, where f, g are analytic functions, the Second Nevanlinna Theorem yields an analogue result as in the mentioned paper. However, if they are meromorphic, non trivial estimates for T(r,f) are more sophisticated.