2017
Том 69
№ 9

All Issues

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

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

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 5, pp 797-814.

Citation Example: Sheremeta M. M., Stets' Yu. V. On the regular growth of Dirichlet series absolutely convergent in a half-plane // Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 686-698.

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