2019
Том 71
№ 9

All Issues

Stets' Yu. V.

Articles: 1
Article (Ukrainian)

On the regular growth of Dirichlet series absolutely convergent in a half-plane

Sheremeta M. M., Stets' Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 686-698

For the Dirichlet series $F(s) = \sum^{\infty}_{n=1}a_n \exp \{s \lambda_n\}$ with the abscissa of absolute convergence $\sigma a = 0$, conditions on $(λ_n)$ and $(a_n)$ (λn) are established under which $\ln M(\sigma, F) = T_R(1 + o(1)) \exp\{\varrho R/|\sigma|\}$ as $\sigma \uparrow 0$, where$M(σ, F) = \sup\{|F(\sigma + it)| : t \in R\}$ and $T_R$ and $\varrho_R$ are positive constants.