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

  • Yu. V. Stets' Львiв. нац. ун-т
  • M. M. Sheremeta Львiв. нац. ун-т


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.
How to Cite
Stets’, Y. V., and M. M. Sheremeta. “On the Regular Growth of Dirichlet Series Absolutely Convergent in a Half-Plane”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 5, May 2011, pp. 686-98, https://umj.imath.kiev.ua/index.php/umj/article/view/2753.
Research articles