On the abscises of the convergence of multiple Dirichlet series

Abstract

For multiple Dirichlet series of the form$F(s)=sum_{|n|=0}^infty a_{(n)}exp{(lambda_{(n)},s)}$ weestablish relations between domains of the convergence $G_c$,absolutely convergence $G_a$ and of the domain of the existence ofthe maximal term $G_{mu}$ of the series as follows: $gammaG_{c}subset G_{a}+delta_0 e_{1}, gamma G_{mu}subsetG_{a}+delta_0 e_{1},$ where $e_{1}=(1,...,1)in mathbb{R}^p,;; delta_0in mathbb{R},$ by condition $varliminflimits_{|n|oinfty}frac{(gamma-1)ln,|a_{(n)}|+delta_0|lambda_{(n)}|}{ln|n|}>p;$$gamma G_csubset G_a+delta; ;; gamma G_{mu}subsetG_a+delta,$ where $deltainmathbb{R}^{p},$ by condition$varliminflimits_{|n|oinfty}frac{(gamma-1)ln,|a_{(n)}|+(delta,lambda_{(n)})}{ln,n_1+...+ln,n_p}>1.$