  We study the hole probability of Gaussian entire functions. More
specifically, we work with entire functions in Taylor series form with i.i.d
complex Gaussian random variables and arbitrary non-random coefficients. A hole
is the event where the function has no zeros in a disc of radius r. We find
exact asymptotics for the rate of decay of the hole probability for large
values of r, outside a small exceptional set. The exceptional set depends only
on the non-random coefficients. We assume no regularity conditions on the
non-random coefficients.
