Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON CERTAIN POLYNOMIALS HAVING ALL THEIR ZEROS EXCEPT FOR 1 ON A CIRCLE OF RADIUS < 1

  • Kim, Seon-Hong (Department of Mathematics, Sookmyung Women's University)
  • Received : 2009.08.13
  • Accepted : 2009.11.06
  • Published : 2009.12.30
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Abstract

Given $\alpha$ > 1, there exist $C(1/\alpha)$-polynomials of the form $z^n-\sum_{k=0}^{n-1}\;a_kz^k$, where $\sum_{k=0}^{n-1}\;a_k=1$, $a_{n-1}>0$ and $a_k{\geq}0$ for each k. In this paper, we obtain lower bounds for $a_{n-1}$.

Keywords

References

  1. S. Dubuc, A. Malik, Convex hull of powers of a complex number, trinomial equations and the Farey sequence, Numer. Algorithms 2 (1992), 1-32. https://doi.org/10.1007/BF02142203
  2. M. Marden, Geometry of Polynomials, Math. Surveys, No. 3, Amer. Math. Society, Providence, R. I., 1966.
  3. S.-H. Kim, Polynomials with weighted sum, Publ. Math. Debrecen 66 (2005), 303-311.