Fluctuations for zeros of Gaussian Taylor series

We study fluctuations in the number of zeros random analytic functions given by a Taylor series whose coefficients are independent complex Gaussians. When entire, we find sharp bounds for asymptotic growth rate variance large disks centered at origin. To obtain result that holds under no assumptions on employ Wiman-Valiron theory. demonstrate sharpness our studying well-behaved covariance kernels, which call admissible (after Hayman).