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The Nevanlinna characteristic and maximum modulus of
entire functions of finite order with random zeros (in Ukrainian) |
| Author |
Yu. B. Zakharko, P. V. Filevych
Ivan Franko national University of L’viv
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| Abstract |
Let $(r_n)$ be a positive nondecreasing sequence of finite genus tending to $+\infty$, and $(\eta_n(\omega))$ be a sequence of independent random variables such that $\eta_n(\omega)$ are uniformly distributed on the circles $|z|=r_n$. Then for almost all $\omega$ the following assertion holds: if $f$ is an entire function of finite order with zeros at the points $\eta_n(\omega)$ and only at them, then for every $\varepsilon>0$ we have $\ln M_f(r)=o(T_f^{3/2}(r)\ln^{3+\varepsilon} T_f(r))$, $r\to+\infty$, where $M_f(r)$ is the maximum modulus and $T_f(r)$ is the Nevanlinna characteristic of the function $f$. |
| Keywords |
entire function of finite order; Nevanlinna characteristic; independent random variables |
| Reference |
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| Pages |
40-50 |
| Volume |
36 |
| Issue |
1 |
| Year |
2011 |
Journal |
Matematychni Studii |
| Full text of paper |
PDF |
| Table of content of issue |
HTML |