On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane - Mikityuk, L. Ya.; Sheremeta, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
For a Dirichlet series \(olimits_n = 1^∞ a_n { sλ_n } \) with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder \(olimits_k = n^∞ | a_k |{ δ λ_k } \) , δ < 0, as n → ∞.