Paley Effect for Entire Dirichlet Series

  • T. Ya. Hlova
  • P. V. Filevych


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 $λ_n$ 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.
How to Cite
Hlova, T. Y., and P. V. Filevych. “Paley Effect for Entire Dirichlet Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 6, June 2015, pp. 739–751,
Research articles