Geodesic
A note on the number of zeros of polynomials in an annulus
Xiangdong Yang1 ; Caifeng Yi2 ; Jin Tu2
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
Annales Polonici Mathematici, Tome 100 (2011) no. 1, pp. 25-31.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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. http://geodesic.mathdoc.fr/articles/10.4064/ap100-1-3/

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