Ukrainian Mathematical Journal

, Volume 56, Issue 11, pp 1782–1795 | Cite as

On the Mean Values of the Dirichlet Series

  • M. M. Zelisko
  • M. M. Sheremeta


For Dirichlet series with arbitrary abscissa of absolute convergence, we investigate the relationhip between the increase in the maximum term and \(\left( {\mathop \sum \nolimits_{n = 1}^\infty \left| {a_n } \right|^q \exp \{ q\sigma \lambda _n \} } \right)^{1/q}\), q ∈ (0,+∞).


Dirichlet Series Absolute Convergence Maximum Term 
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  1. 1.
    A. F. Leont’ev, Exponential Series [in Russian], Nauka, Moscow (1976).Google Scholar
  2. 2.
    F. I. Geche and S. V. Opinchuk, “On the abscissas of convergence of the Dirichlet series and its Newton majorant,” Ukr. Mat. Zh., 26, No.2, 161–168 (1974).Google Scholar
  3. 3.
    M. M. Sheremeta, Entire Dirichlet Series [in Ukrainian], ISDO, Kyiv (1993).Google Scholar
  4. 4.
    A. A. Gol’dberg and I. V. Ostrovskii, Distribution of Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. M. Zelisko
    • 1
  • M. M. Sheremeta
    • 1
  1. 1.Lviv National UniversityLvivUkraine

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