A note on the number of zeros of polynomials in an annulus
Xiangdong Yang ; Caifeng Yi ; Jin Tu
Annales Polonici Mathematici, Tome 101 (2011), p. 25-31 / Harvested from The Polish Digital Mathematics Library
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Let p(z) be a polynomial of the form p(z)=∑j=0najzj, aj∈-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.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:280665 
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     title = {A note on the number of zeros of polynomials in an annulus},
     journal = {Annales Polonici Mathematici},
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     year = {2011},
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     zbl = {1246.30005},
     language = {en},
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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 101 (2011) pp. 25-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-1-3/