On roots of polynomials with power series coefficients

Volume 80 / 2003

Rafał Pierzchała Annales Polonici Mathematici 80 (2003), 211-217 MSC: Primary 13F25; Secondary 32B20, 16W60. DOI: 10.4064/ap80-0-18


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.


  • Rafał PierzchałaInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland

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