Bergweiler-Langley lemmas in several complex variables

Source abstract

The main objective of this paper is to estimate asymptotic property of the logarithmic differences of a transcendental meromorphic function of order less than $1$ in several complex variables. The results extend the fundamental lemmas of Bergweiler and Langley in several complex variables. As an application of our main results, we estimate the growth of entire solutions in $\mathbb{C}^m$ of a certain type of complex linear difference equation.