Journal of Integrative Natural Science (통합자연과학논문집)

The Basic Science Institute Chosun University (조선대학교 기초과학연구원)
권호 표지
DOI QR코드

DOI QR Code

On Some Polynomials with Weighted Sums

  • Received : 2017.01.18
  • Accepted : 2017.03.25
  • Published : 2017.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this note, we study a generalization of a certain polynomial $z^n-{\sum\limits_{k=0}^{n-1}}a_kz^k$, where $\sum\limits_{k=0}^{n-1}a_k=1$, $a_k{\geq}0$ for each k, whose all zeros except for z=1 lie on the circle of radius 1/2 with center at the origin.

Keywords

References

  1. M. Marden, "Geometry of polynomials, mathe- matical surveys number 3", American Mathematical Society, Providence, Rhode Island, p. 136, 1966.
  2. S.-H. Kim, "Polynomials with weighted sum", Publ. Math-Debrecen, Vol. 66, pp. 303-311, 2005.
  3. T. Sheil-Small, "Complex polynomials", Cambridge University Press, Cambridge, p. 230, 2002.