A Measure of Linear Independence for Some Exponential Functions II

Abstract

This paper continues the investigations in [1] and [2] and extends the results of the latter paper to functions of several complex variables. Namely let λ : R>0 —> R>0 be monotonically increasing. (If λ is non-constant, we also require that log r = 0(λ(r)). We write / = 0(g) to mean that there is a constant C > 0 such that f(r) ≦ Cg(r) except possibly on a set of intervals of finite total length.) Let 0\ denote the set of meromorphic / on Cn for which the Nevanlinna characteristic function [5, p. 174] T(f, r) satisfies T(f, r) = 0(λ(r)).