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 \(\sum olimits_{n = 1}^∞ {a_n \exp \{ sλ_n \} } \) with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder \(\sum olimits_{k = n}^∞ {\left| {a_k } \right|\exp \{ {δ λ}_k \} } \) , δ < 0, as n → ∞.