A note on the number of zeros of polynomials in an annulus

Xiangdong Yang, Caifeng Yi, and Jin Tu. "A note on the number of zeros of polynomials in an annulus." Annales Polonici Mathematici 100.1 (2011): 25-31. <http://eudml.org/doc/280665>.

@article{XiangdongYang2011,
abstract = {Let p(z) be a polynomial of the form $p(z) = ∑_\{j=0\}^\{n\} a_\{j\}z^\{j\}$, $a_\{j\} ∈ \{-1,1\}$. We discuss a sufficient condition for the existence of zeros of p(z) in an annulus z ∈ ℂ: 1 - c < |z| < 1 + c, where c > 0 is an absolute constant. This condition is a combination of Carleman’s formula and Jensen’s formula, which is a new approach in the study of zeros of polynomials.},
author = {Xiangdong Yang, Caifeng Yi, Jin Tu},
journal = {Annales Polonici Mathematici},
keywords = {number of zeros; polynomial in an annulus},
language = {eng},
number = {1},
pages = {25-31},
title = {A note on the number of zeros of polynomials in an annulus},
url = {http://eudml.org/doc/280665},
volume = {100},
year = {2011},
}

TY - JOUR
AU - Xiangdong Yang
AU - Caifeng Yi
AU - Jin Tu
TI - A note on the number of zeros of polynomials in an annulus
JO - Annales Polonici Mathematici
PY - 2011
VL - 100
IS - 1
SP - 25
EP - 31
AB - Let p(z) be a polynomial of the form $p(z) = ∑_{j=0}^{n} a_{j}z^{j}$, $a_{j} ∈ {-1,1}$. We discuss a sufficient condition for the existence of zeros of p(z) in an annulus z ∈ ℂ: 1 - c < |z| < 1 + c, where c > 0 is an absolute constant. This condition is a combination of Carleman’s formula and Jensen’s formula, which is a new approach in the study of zeros of polynomials.
LA - eng
KW - number of zeros; polynomial in an annulus
UR - http://eudml.org/doc/280665
ER -