Geodesic
A note on the number of zeros of polynomials in an annulus
Xiangdong Yang1 ; Caifeng Yi2 ; Jin Tu2
1Department of Mathematics Kunming University of Science and Technology 650093 Kunming, China
2College of Mathematics and Information Sciences Jiangxi Normal University 330022 Nanchang, China
Annales Polonici Mathematici, Tome 100 (2011) no. 1, pp. 25-31
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Let $p(z)$ be a polynomial of the form $$ p(z)=\sum_{j=0}^{n}a_{j} z^{j},\quad\ a_{j}\in \{-1, 1\}. $$ We discuss a sufficient condition for the existence of zeros of $p(z)$ in an annulus $$\{z\in \mathbb{C}: 1- c|z| 1+c\},$$ 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.
DOI : 10.4064/ap100-1-3
Keywords: polynomial form sum quad discuss sufficient condition existence zeros annulus mathbb where absolute constant condition combination carlemans formula jensens formula which approach study zeros polynomials

Xiangdong Yang  1   ; Caifeng Yi  2   ; Jin Tu  2

1 Department of Mathematics Kunming University of Science and Technology 650093 Kunming, China
2 College of Mathematics and Information Sciences Jiangxi Normal University 330022 Nanchang, China 
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Xiangdong Yang; Caifeng Yi; Jin Tu. A note on the number of zeros of polynomials in an annulus. Annales Polonici Mathematici, Tome 100 (2011) no. 1, pp. 25-31. doi: 10.4064/ap100-1-3

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