Location of the critical points of certain polynomials
Somjate Chaiya; Aimo Hinkkanen
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2013)
- Volume: 67, Issue: 2
- ISSN: 0365-1029
Access Full Article
topAbstract
topHow to cite
topSomjate Chaiya, and Aimo Hinkkanen. "Location of the critical points of certain polynomials." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 67.2 (2013): null. <http://eudml.org/doc/289781>.
@article{SomjateChaiya2013,
abstract = {Let $\mathbb \{D\}$ denote the unit disk $\lbrace z:|z|<1\rbrace $ 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 $P^\{\prime \}$ has exactly one critical point outside $\overline\{\mathbb \{D\}\}$.},
author = {Somjate Chaiya, Aimo Hinkkanen},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Polynomial; critical point; anti-reciprocal.},
language = {eng},
number = {2},
pages = {null},
title = {Location of the critical points of certain polynomials},
url = {http://eudml.org/doc/289781},
volume = {67},
year = {2013},
}
TY - JOUR
AU - Somjate Chaiya
AU - Aimo Hinkkanen
TI - Location of the critical points of certain polynomials
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2013
VL - 67
IS - 2
SP - null
AB - Let $\mathbb {D}$ denote the unit disk $\lbrace z:|z|<1\rbrace $ 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 $P^{\prime }$ has exactly one critical point outside $\overline{\mathbb {D}}$.
LA - eng
KW - Polynomial; critical point; anti-reciprocal.
UR - http://eudml.org/doc/289781
ER -
References
top- 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.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.