For the Dirichlet series \( F(s) = \sum\nolimits_{n = 1}^\infty {{a_n}\exp \left\{ {s{\lambda_n}} \right\}} \) with abscissa of absolute convergence σ a =0, we establish conditions for (λ n ) and (a n ) under which \( \ln M\left( {\sigma, F} \right) = {T_R}\left( {1 + o(1)} \right)\exp \left\{ {{{{{\varrho_R}}} \left/ {{\left| \sigma \right|}} \right.}} \right\} \) for σ ↑ 0, where \( M\left( {\sigma, F} \right) = \sup \left\{ {\left| {F\left( {\sigma + it} \right)} \right|:t \in \mathbb{R}} \right\} \) and T R and ϱ R are positive constants.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 5, pp. 686–698, May, 2011.
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Stets’, Y.V., Sheremeta, M.M. On the regular growth of Dirichlet series absolutely convergent in a half-plane. Ukr Math J 63, 797–814 (2011). https://doi.org/10.1007/s11253-011-0543-7
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DOI: https://doi.org/10.1007/s11253-011-0543-7