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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
Article
  • 18 Downloads

Abstract

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,+∞).

Keywords

Dirichlet Series Absolute Convergence Maximum Term 
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REFERENCES

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    A. F. Leont’ev, Exponential Series [in Russian], Nauka, Moscow (1976).Google Scholar
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    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
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    M. M. Sheremeta, Entire Dirichlet Series [in Ukrainian], ISDO, Kyiv (1993).Google Scholar
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    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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