On the "pits effect" of Littlewood and Offord
Complex Variables
2021-12-21 v2
Abstract
Suppose that the moduli of the coefficients of a power series are 1/n!, while the arguments are arbitrary. If an entire function f represented by such power series decreases exponentially on some ray, then it has to be an exponential. If the arguments of the coefficients are of the form 2pi n^2a, where a is irrational, then the function displays the so-called "pits effect". More precisely, under this condition, f is of completely regular growth with constant indicator.
Keywords
Cite
@article{arxiv.0710.2870,
title = {On the "pits effect" of Littlewood and Offord},
author = {Alexandre Eremenko and Iossif Ostrovskii},
journal= {arXiv preprint arXiv:0710.2870},
year = {2021}
}
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17 pages