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Ukrainian Mathematical Journal

, Volume 55, Issue 3, pp 456–467 | Cite as

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

  • L. Ya. Mykytyuk
  • M. M. Sheremeta
Article
  • 29 Downloads

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 → ∞.

Keywords

Asymptotic Behavior Dirichlet Series Absolute Convergence Nonnegative Exponent 
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REFERENCES

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • L. Ya. Mykytyuk
  • M. M. Sheremeta

There are no affiliations available

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