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

We study the influence the angular distribution of zeroes of the Taylor

series with pseudo-random and random coefficients, and show that the

distribution of zeroes is governed by certain autocorrelations of the

coefficients. Using this guiding principle, we consider several examples

of random and pseudo-random sequences $\xi$ and, in particular, answer

some questions posed by Chen and Littlewood in 1967.

As a by-product we show that if $\xi$ is a stationary random

integer-valued sequence, then either it is periodic, or its spectral

measure has no gaps in its support. The same conclusion is true if $\xi$

is a complex-valued stationary ergodic sequence that takes values from a

uniformly discrete set (joint work with Alexander Borichev and Alon Nishry).

- Last modified: 18/11/2014