On the abscises of the convergence of multiple Dirichlet series - Zadorozhna, O.Yu.; Skaskiv, O.B. (Carpathian Mathematical Publications, 2009)
For multiple Dirichlet series of the form $F(s)=\sum_{\|n\|=0}^∞ a_{(n)}\exp\{(λ_{(n)},s)\}$ we establish relations between domains of the convergence $G_c$, absolutely convergence $G_a$ and of the domain of the existence of the maximal term $G_{μ}$ of the series as follows: $γ G_{c}\subset G_{a}+δ_0 e_{1},\ γ G_{μ}\subset G_{a}+δ_0 e_{1},$ where $e_{1}=(1,…,1)\in \mathbb{R}^p, \;\; δ_0\in \mathbb{R},$ by condition $ \varliminf\limits_{\|n\|→∞} \frac{(γ-1)\ln\,|a_{(n)}|+δ_0\|λ_{(n)}\|}{\ln\|n\|}>p;$ $γ G_c\subset G_a+δ; \;\; γ G_{μ}\subset G_a+δ,$ where $δ\in\mathbb{R}^{p},$ by condition $\varliminf\limits_{\|n\|→∞} \frac{(γ-1)\ln\,|a_{(n)}|+(δ,λ_{(n)})}{\ln\,n_1+...+\ln\,n_p}>1.$