Minimum of the multiple Dirichlet series
Conditions are established under which the following relation is satisfied: $$M (x) = (1 + o (1)) m (x) = (1 + o (1)) \mu (x)$$ as $| x |\rightarrow + \infty$ outside a sufficiently small set, for an entire function $F (z)$ of several complex variables $z\in\mathbb{C}^p$, $p\geq 2$, represented by a...
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8187 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | Conditions are established under which the following relation is satisfied:
$$M (x) = (1 + o (1)) m (x) = (1 + o (1)) \mu (x)$$
as $| x |\rightarrow + \infty$ outside a sufficiently small set, for an entire function $F (z)$ of several complex variables $z\in\mathbb{C}^p$, $p\geq 2$, 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 $\mu (x)$ the maximal term of the Dirichlet series, $x \in \mathbb{R}^p$. |
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