On n-member asymptotics for logarithm of maximal term of entire Dirichlet series

For an entire Dirichlet series with positive increasing to $+\infty$ exponents, conditions on coefficients under which $\ln \mu(\sigma)=\sum_{j=1}^{n-1} T_j e^{r_j\sigma} +(\tau +o(1))e^{r_n\sigma}$, $(\sigma\to+\infty)$, $n\ge 2$, where $\mu(\sigma) =\max\{|a_n| \exp(\sigma \lambda_n):n\ge 0\}$ is the maximal term of the series and $\rho_n< \dots\ \rho_2<\rho_1<+\infty$, $T_1>0$, $T_j\in \Bbb R$, $(j=2, \dots, n-1)$, $\tau\in \Bbb R$, $n\ge 2$, $\rho_2<(\rho_1+\rho_n)/2$, are established.