REMARKS TO RELATIVE GROWTH OF ENTIRE DIRICHLET SERIES

Анотація

Let $F$ and $G$ be entire functions given by Dirichlet series with exponents increasing to $+\infty$ and $\varrho_R[F]_G$ be
the $R$-order of $F$ with respect to a function $G$. The quantities
$$
T_R[F]_G:=\varlimsup\limits_{\sigma\to+\infty}\dfrac{\exp\{ M^{-1}_G(M_F(\sigma))\}}{\exp\{\varrho_R[F]_G \sigma\}}, \quad
t_R[F]_G:=\varliminf\limits_{\sigma\to+\infty}\dfrac{\exp\{ M^{-1}_G(M_F(\sigma))\}}{\exp\{\varrho_R[F]_G \sigma\}}
$$
we will call the $R$-type and the lower $R$-type of $F$ with respect to $G$. A connection between $T_R[F]_G$, $t_R[F]_G$ and the
$R$-types and the lower $R$-types of $F$ and $G$ is shown