Paley Effect for Entire Dirichlet Series
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 $$\underset{r\to +\infty }{ \lim \sup}\frac{ \ln {M}_f(r)}{T_f(r)}...
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| Date: | 2015 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2015
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2018 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | For the entire Dirichlet series $f(z) = ∑_{n = 0}${∞$ a_n e^{zλn}$, we establish necessary and sufficient conditions on the coefficients $a_n$ and exponents $λ_n$ under which the function $f$ has the Paley effect, i.e., the condition
$$\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. |
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