The Nevanlinna characteristic and maximum modulus of entire functions of finite order with random zeros (in Ukrainian)

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 $ln M_f(r)=o(T_f^{3/2}(r)ln^{3+varepsilon} T_f(r))$, $rto+infty$, where $M_f(r)$ is the maximum modulus and $T_f(r)$ is the Nevanlinna characteristic of the function $f$.