On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane

• Datum: 2003
• Hauptverfasser: Mikityuk, L. Ya., Sheremeta, M. M., Микитюк, Л. Я., Шеремета, М. М.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2003
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3912
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

For a Dirichlet series \(\sum\nolimits_{n = 1}^\infty {a_n \exp \{ s{\lambda}_n \} } \) with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder \(\sum\nolimits_{k = n}^\infty {\left| {a_k } \right|\exp \{ {\delta \lambda}_k \} } \...