Location of the critical points of certain polynomials

• Autorzy: Somjate Chaiya , Aimo Hinkkanen
• Języki publikacji: EN

Abstrakty

EN

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 \(\overline{\mathbb{D}}\).

Słowa kluczowe

EN

Polynomial; critical point; anti-reciprocal.

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2013
• Tom: 67
• Numer: 2

Daty

wydano

2013

online

2015-07-15

Twórcy

autor

Somjate Chaiya

autor

Aimo Hinkkanen

Bibliografia

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• Chaiya, S., Complex dynamics and Salem numbers, Ph.D. Thesis, University of Illinois at Urbana–Champaign, 2008.
• Palka, Bruce P., An Introduction to Complex Function Theory, Springer-Verlag, New York, 1991.
• Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002.
• Salem, R., Power series with integral coefficients, Duke Math. J. 12 (1945), 153–173.
• Salem, R., Algebraic Numbers and Fourier Analysis, D. C. Heath and Co., Boston, Mass., 1963.
• Sheil-Small, T., Complex Polynomials, Cambridge University Press, Cambridge, 2002.
• Walsh, J. L., Sur la position des racines des derivees d’un polynome, C. R. Acad. Sci. Paris 172 (1921), 662–664.

Identyfikatory

DOI

10.17951/a.2013.67.2.1-9