Minimum of the multiple Dirichlet series - Skaskiv , О. B.; Lutsishin , M. R. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
Conditions are established under which the following relation is satisfied:$$M (x) = (1 + o (1)) m (x) = (1 + o (1)) μ (x)$$as $| x |→ + ∞$ outside a sufficiently small set, for an entire function $F (z)$ of several complex variables $z\in\mathbb{C}^p$, $p≥ 2$, represented by a Dirichlet series. Here $M (x) = \rm{sup}\{| F (x + iy)| : y \in \mathbb{R}^p\}$ and $m (x) =\rm{ inf} \{ | F (x + iy) | : y \in \mathbb{R}^p\}$, with $μ (x)$ the maximal term of the Dirichlet series, $x \in \mathbb{R}^p$.