Year: 2021
Type: preprint
Abstract: Ostrovskii's generalization of the Marcinkiewicz theorem implies that if an entire characteristic functions of a probability distribution satisfies $\log^+\log|f(z)|=o(|z|),\; z\to\infty,$ and is zero-free then the distribution is normal. We show that under the same growth condition, absence of zeros in a wide vertical strip implies that the distribution is close to a normal one. This generalizes and simplifies a recent result of Michelen and Sahasrabudhe.
Source: arXiv (Cornell University)
Authors: Eremenko, Alexandre, Fryntov, Alexander
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3177053623