Let denote the unit disk in the complex plane . In this paper, we study a family of polynomials with only one zero lying outside . We establish criteria for to satisfy implying that each of and has exactly one critical point outside .
@article{bwmeta1.element.ojs-doi-10_17951_a_2013_67_2_1-9,
author = {Somjate Chaiya and Aimo Hinkkanen},
title = {Location of the critical points of certain polynomials},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {67},
year = {2013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2013_67_2_1-9}
}
Somjate Chaiya; Aimo Hinkkanen. Location of the critical points of certain polynomials. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 67 (2013) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2013_67_2_1-9/
Boyd, D. W., Small Salem numbers, Duke Math. J. 44 (1977), 315–328.
Bertin, M. J., Decomps-Guilloux, A., Grandet-Hugot, M., Pathiaux-Delefosse, M., Schreiber, J. P., Pisot and Salem Numbers, Birkhauser Verlag, Basel, 1992.
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.