Location of the critical points of certain polynomials

Somjate Chaiya; Aimo Hinkkanen

Annales UMCS, Mathematica (2013)

  • Volume: 67, Issue: 2, page 1-9
  • ISSN: 2083-7402

Abstract

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

How to cite

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Somjate Chaiya, and Aimo Hinkkanen. "Location of the critical points of certain polynomials." Annales UMCS, Mathematica 67.2 (2013): 1-9. <http://eudml.org/doc/267618>.

@article{SomjateChaiya2013,
abstract = {Let D¯ denote the unit disk \{z : |z| < 1\} in the complex plane C. In this paper, we study a family of polynomials P with only one zero lying outside D¯. We establish criteria for P to satisfy implying that each of P and P' has exactly one critical point outside D¯.},
author = {Somjate Chaiya, Aimo Hinkkanen},
journal = {Annales UMCS, Mathematica},
keywords = {Polynomial; critical point; anti-reciprocal; polynomials; zeros; critical points},
language = {eng},
number = {2},
pages = {1-9},
title = {Location of the critical points of certain polynomials},
url = {http://eudml.org/doc/267618},
volume = {67},
year = {2013},
}

TY - JOUR
AU - Somjate Chaiya
AU - Aimo Hinkkanen
TI - Location of the critical points of certain polynomials
JO - Annales UMCS, Mathematica
PY - 2013
VL - 67
IS - 2
SP - 1
EP - 9
AB - Let D¯ denote the unit disk {z : |z| < 1} in the complex plane C. In this paper, we study a family of polynomials P with only one zero lying outside D¯. We establish criteria for P to satisfy implying that each of P and P' has exactly one critical point outside D¯.
LA - eng
KW - Polynomial; critical point; anti-reciprocal; polynomials; zeros; critical points
UR - http://eudml.org/doc/267618
ER -

References

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  1. [1] Boyd, D. W., Small Salem numbers, Duke Math. J. 44 (1977), 315-328.[Crossref] 
  2. [2] Bertin, M. J., Decomps-Guilloux, A., Grandet-Hugot, M., Pathiaux-Delefosse, M., Schreiber, J. P., Pisot and Salem Numbers, Birkh¨auser Verlag, Basel, 1992.[WoS] 
  3. [3] Chaiya, S., Complex dynamics and Salem numbers, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2008. 
  4. [4] Palka, Bruce P., An Introduction to Complex Function Theory, Springer-Verlag, New York, 1991. Zbl0726.30001
  5. [5] Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002. Zbl1072.30006
  6. [6] Salem, R., Power series with integral coefficients, Duke Math. J. 12 (1945), 153-173.[Crossref] 
  7. [7] Salem, R., Algebraic Numbers and Fourier Analysis, D. C. Heath and Co., Boston, Mass., 1963. Zbl0126.07802
  8. [8] Sheil-Small, T., Complex Polynomials, Cambridge University Press, Cambridge, 2002. Zbl1012.30001
  9. [9] Walsh, J. L., Sur la position des racines des d´eriv´ees d’un polynome, C. R. Acad. Sci. Paris 172 (1921), 662-664. Zbl48.0086.01

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