On roots of polynomials with power series coefficients

Rafał Pierzchała. "On roots of polynomials with power series coefficients." Annales Polonici Mathematici 80.1 (2003): 211-217. <http://eudml.org/doc/280233>.

@article{RafałPierzchała2003,
abstract = {We give a deepened version of a lemma of Gabrielov and then use it to prove the following fact: if h ∈ 𝕂[[X]] (𝕂 = ℝ or ℂ) is a root of a non-zero polynomial with convergent power series coefficients, then h is convergent.},
author = {Rafał Pierzchała},
journal = {Annales Polonici Mathematici},
keywords = {formal power series; convergent power series; Newton-Puiseux theorem; roots of polynomials},
language = {eng},
number = {1},
pages = {211-217},
title = {On roots of polynomials with power series coefficients},
url = {http://eudml.org/doc/280233},
volume = {80},
year = {2003},
}

TY - JOUR
AU - Rafał Pierzchała
TI - On roots of polynomials with power series coefficients
JO - Annales Polonici Mathematici
PY - 2003
VL - 80
IS - 1
SP - 211
EP - 217
AB - We give a deepened version of a lemma of Gabrielov and then use it to prove the following fact: if h ∈ 𝕂[[X]] (𝕂 = ℝ or ℂ) is a root of a non-zero polynomial with convergent power series coefficients, then h is convergent.
LA - eng
KW - formal power series; convergent power series; Newton-Puiseux theorem; roots of polynomials
UR - http://eudml.org/doc/280233
ER -