Entire Gaussian Functions: Probability of Zeros Absence

In this paper, we consider a random entire function of the form f(z,?)=?n=0+??n(?1)×?n(?2)fnzn, where (?n) is sequence independent Steinhaus variables, (?n) standard complex Gaussian and numbers fn?C such that lim¯n?+?|fn|n=0 #{n:fn?0}=+?. We investigate asymptotic estimates probability P0(r)=P{?:f(z,?) has no zeros inside rD} as r?+? outside some set E finite logarithmic measure, i.e., ?E?[1,+?)dlnr<+?. The obtained for absence functions are in certain sense best possible result. Furthermore, give an answer to open question A. Nishry functions.