The q -Difference Theorems for Meromorphic Functions of Several Variables

Abstract EN

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 ) ≠ 0 , ∞ , and let q ∈ ℂ n \ { 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.