# 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

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topSomjate 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

top- [1] Boyd, D. W., Small Salem numbers, Duke Math. J. 44 (1977), 315-328.[Crossref]
- [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] Chaiya, S., Complex dynamics and Salem numbers, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2008.
- [4] Palka, Bruce P., An Introduction to Complex Function Theory, Springer-Verlag, New York, 1991. Zbl0726.30001
- [5] Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002. Zbl1072.30006
- [6] Salem, R., Power series with integral coefficients, Duke Math. J. 12 (1945), 153-173.[Crossref]
- [7] Salem, R., Algebraic Numbers and Fourier Analysis, D. C. Heath and Co., Boston, Mass., 1963. Zbl0126.07802
- [8] Sheil-Small, T., Complex Polynomials, Cambridge University Press, Cambridge, 2002. Zbl1012.30001
- [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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