A note on the number of zeros of polynomials in an annulus
Tom 100 / 2011
Annales Polonici Mathematici 100 (2011), 25-31
MSC: Primary 30B30; Secondary 11C08, 30C15.
DOI: 10.4064/ap100-1-3
Streszczenie
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.
