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Ukrainian Mathematical Journal

, Volume 57, Issue 4, pp 686–693 | Cite as

On the Stability of the Maximum Term of the Entire Dirichlet Series

  • O. B. Skaskiv
  • O. M. Trakalo
Article
  • 20 Downloads

Abstract

We establish necessary and sufficient conditions for the logarithms of the maximum terms of the entire Dirichlet series \(F(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n e^{z\lambda _n } }\) and \(B(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n b_n e^{z\lambda _n } }\) to be asymptotically equivalent as Re z → +∞ outside a certain set of finite measure.

Keywords

Dirichlet Series Finite Measure Maximum Term Entire Dirichlet Series 
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REFERENCES

  1. 1.
    A. M. Gaisin, “Estimate for the Dirichlet series with Fejer lacunas,” Dokl. Ros. Akad. Nauk, 370, No.6, 735–737 (2000).Google Scholar
  2. 2.
    O. B. Skaskiv, “On the behavior of the maximum term of a Dirichlet series that defines an entire function,” Mat. Zametki, 37, No.1, 41–47 (1985).Google Scholar
  3. 3.
    O. B. Skaskiv, “On some relations between the maximum of the modulus and the maximum term of the entire Dirichlet series,” Mat. Zametki, 56, No.2, 282–292 (1999).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • O. B. Skaskiv
    • 1
  • O. M. Trakalo
    • 1
  1. 1.Lviv National UniversityLvivUkraine

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