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 ${ℂ}^n$ of zero order such that $f(0)\ne 0$, $\infty$, and let $q\in {ℂ}^n\backslash \{0\}$. 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.