2019
Том 71
№ 11

All Issues

Lutsyshyn M. R.

Articles: 1
Brief Communications (Ukrainian)

Minimum of modulus of dirichlet multisequence

Lutsyshyn M. R., Skaskiv O. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1295–1297

Conditions are established under which the following relation is satisfied: $$M(x) = (1 + o(1))m(x) = (1 + o(1))\mu (x)$$ as $|x |→ + ∞$ outside a sufficiently small set, for an entire function $F(z)$ of several complex variables $z ∈ ℂ_p,p ≥ 2$, represented by a Dirichlet series. Here $M(x) = \sup \{|F(x+iy) |: y ∈ ℝ^p\}$ and $m(x) = \inf \{ |F(x+iy) |:y ∈ ℝ^p,$ with $μ(x)$ the maximal term of the Dirichlet series, $x ∈ ℝ^p$.