Zeros of sections of power series: deterministic and random
Complex Variables
2016-12-05 v2 Probability
Abstract
We present a streamlined proof (and some refinements) of a characterization (due to F. Carlson and G. Bourion, and also to P. Erd\"os and H. Fried) of the so called Szeg\"o's power series. This characterization is then applied to readily obtain some (more) recent known results and some new results on the asymptotic distribution of zeros of sections of random power series, extricating quite naturally the deterministic ingredients. Finally, we study the possible limits of the zero counting probabilities of a power series.
Keywords
Cite
@article{arxiv.1507.02843,
title = {Zeros of sections of power series: deterministic and random},
author = {José L. Fernández},
journal= {arXiv preprint arXiv:1507.02843},
year = {2016}
}