Entire functions of exponential type represented by pseudo-random and random Taylor series

Alexander Borichev, Alon Nishry, Mikhail Sodin

We study the influence of the multipliers $\xi (n)$ on the angular distribution of zeroes of the Taylor series \[ F_ξ(z) = \sum_{n\ge 0} ξ(n) \frac{z^n}{n!}\,. \] We show that the dis…