Location of the critical points of certain polynomials

Somjate Chaiya, Aimo Hinkkanen


Let \(\mathbb{D}\) denote the unit disk \(\{z:|z|<1\}\) in the complex plane \(\mathbb{C}\). In this paper, we study a family of polynomials \(P\) with only one zero lying outside \(\overline{\mathbb{D}}\).  We establish  criteria for \(P\) to satisfy implying that each of \(P\) and \(P'\)  has exactly one critical point outside \(\overline{\mathbb{D}}\).


Polynomial; critical point; anti-reciprocal.

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DOI: http://dx.doi.org/10.17951/a.2013.67.2.1-9
Data publikacji: 2015-07-15 00:00:00
Data złożenia artykułu: 2016-01-12 08:54:40


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