On the geometric means of entire functions of several complex variables

Abstract:

Let $f({z_1}, \ldots ,{z_n})$ be an entire function of the $n( \geqq 2)$ complex variables ${z_1}, \ldots ,{z_n}$, holomorphic for $|{z_t}| \leqq {r_t},t = 1, \ldots ,n$. We have considered the case of only two complex variables for simplicity. Recently many authors have defined the arithmetic means of the function $|f({z_1},{z_2})|$ and have investigated their properties. In the present paper, the geometric means of the function $|f({z_1},{z_2})|$ have been defined and the asymptotic behavior of certain growth indicators for entire functions of several complex variables have been studied and the results are given in the form of theorems.