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Paley Effect for Entire Dirichlet Series

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Ukrainian Mathematical Journal Aims and scope

For the entire Dirichlet series f(z) = ∑ ∞ n = 0 a n e zλn, we establish necessary and sufficient conditions on the coefficients a n and exponents λn under which the function f has the Paley effect, i.e., the condition

$$ \underset{r\to +\infty }{ \lim \sup}\frac{ \ln {M}_f(r)}{T_f(r)}=+\infty $$

is satisfied, where M f (r) and T f (r) are the maximum modulus and the Nevanlinna characteristic of the function f, respectively.

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Authors and Affiliations

  1. Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    T. Ya. Hlova

  2. Stefanyk Pre-Carpathian National University, Ivano-Frankivs’k, Ukraine

    P. V. Filevych

Authors
  1. T. Ya. Hlova
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  2. P. V. Filevych
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 6, pp. 739–751, June, 2015.

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Hlova, T.Y., Filevych, P.V. Paley Effect for Entire Dirichlet Series. Ukr Math J 67, 838–852 (2015). https://doi.org/10.1007/s11253-015-1117-x

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  • DOI: https://doi.org/10.1007/s11253-015-1117-x

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