The q-Difference Theorems for Meromorphic Functions of Several Variables

Abstract

We investigate q-shift analogue of the lemma on logarithmic derivative of several variables. Let f be a meromorphic function in ℂn of zero order such that f(0)≠0, ∞, and let q∈ℂn\{0}. Then we have m(r,f(qz)/f(z))=o(T(r,f)) on a set of logarithmic density 1. The q-shift analogue of the first and the second main theorems of Nevanlinna theory of several variables and their applications is also shown.