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

• Autorzy: Xiangdong Yang , Caifeng Yi , Jin Tu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11C08: Polynomials
• 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
• 30B30: Boundary behavior of power series, over-convergence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2011
• Tom: 100
• Numer: 1
• Strony: 25-31

Daty

wydano

2011

Twórcy

autor

Xiangdong Yang

• Department of Mathematics, Kunming University of Science and Technology, 650093 Kunming, China

autor

Caifeng Yi

• College of Mathematics and Information Sciences, Jiangxi Normal University, 330022 Nanchang, China

autor

Jin Tu

• College of Mathematics and Information Sciences, Jiangxi Normal University, 330022 Nanchang, China

Identyfikatory

DOI

10.4064/ap100-1-3