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


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.


Dirichlet Series Finite Measure Maximum Term Entire Dirichlet Series 
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    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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