Paley Effect for Entire Dirichlet Series

• Date: 2015
• Main Authors: Hlova, T. Ya., Filevych, P. V., Глова, Т. Я., Філевич, П. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2018
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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)}...