2017
Том 69
№ 9

All Issues

Paley Effect for Entire Dirichlet Series

Filevych P. V., Hlova T. Ya.


Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 6, pp 838-852.

Citation Example: Filevych P. V., Hlova T. Ya. Paley Effect for Entire Dirichlet Series // Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 739–751.