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

  • L. Ya. Mikityuk
  • M. M. Sheremeta Львiв. нац. ун-т

Abstract

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 \(\sum\nolimits_{k = n}^\infty {\left| {a_k } \right|\exp \{ {\delta \lambda}_k \} } \) , δ < 0, as n → ∞.
Published
25.03.2003
How to Cite
MikityukL. Y., and SheremetaM. M. “On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 3, Mar. 2003, pp. 379-88, https://umj.imath.kiev.ua/index.php/umj/article/view/3912.
Section
Research articles