On roots of polynomials with power series coefficients
Volume 80 / 2003
Annales Polonici Mathematici 80 (2003), 211-217
MSC: Primary 13F25; Secondary 32B20, 16W60.
DOI: 10.4064/ap80-0-18
Abstract
We give a deepened version of a lemma of Gabrielov and then use it to prove the following fact: if $h \in {{\mathbb K}}[[X]]$ (${{\mathbb K}} = {{\mathbb R}}$ or ${{\mathbb C}}$) is a root of a non-zero polynomial with convergent power series coefficients, then $h$ is convergent.
