Pseudostarlikeness and Pseudoconvexity of Multiple Dirichlet Series

Abstract

Let $p\in {\Bbb N}$, $s=(s_1,...,s_p)\in {\Bbb C}^p$, $h=(h_1,...,h_p)\in {\Bbb R}^p_+$, $(n)=(n_1,...,n_p)\in {\Bbb N}^p$ and the sequences $\lambda_{(n)}=(\lambda^{(1)}_{n_1},...,\lambda^{(p)}_{n_p})$ are such that $0h}f_{(n)}\exp\{(\lambda_{(n)},s)\}$ absolutely converges in $\Pi^p_0=\{s:\text{Re}\,s