@article{e899521251e54d0aaa46c09d1984b435,
title = "Fluctuations for zeros of Gaussian Taylor series",
abstract = "We study fluctuations in the number of zeros of random analytic functions given by a Taylor series whose coefficients are independent complex Gaussians. When the functions are entire, we find sharp bounds for the asymptotic growth rate of the variance of the number of zeros in large disks centered at the origin. To obtain a result that holds under no assumptions on the variance of the Taylor coefficients, we employ the Wiman–Valiron theory. We demonstrate the sharpness of our bounds by studying well-behaved covariance kernels, which we call admissible (after Hayman).",
keywords = "30B20 (primary), 30C15 (secondary)",
author = "Avner Kiro and Alon Nishry",
note = "Publisher Copyright: {\textcopyright} 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",
year = "2021",
month = oct,
doi = "10.1112/jlms.12457",
language = "אנגלית",
volume = "104",
pages = "1172--1203",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "John Wiley and Sons Ltd",
number = "3",
}