The \(q\)-difference theorems for meromorphic functions of several variables (Q1724853)

Summary: We investigate \(q\)-shift analogue of the lemma on logarithmic derivative of several variables. Let \(f\) be a meromorphic function in \(\mathbb C^n\) of zero order such that \(f(0) \neq 0\), \(\infty\), and let \(q \in \mathbb C^n \backslash \{0 \}\). Then we have \(m(r, f(q z) / f(z)) = o(T(r, f))\) 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.