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Location of the Zeros of Certain Complex-Valued Harmonic Polynomials

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  • Hunduma Legesse Geleta
  • Oluma Ararso Alemu
  • Firdous A. Shah

Abstract

Finding the approximate region containing all the zeros of analytic polynomials is a well-studied problem. But the number of the zeros and regions containing all the zeros of complex-valued harmonic polynomials is relatively a fresh research area. It is well known that all the zeros of analytic trinomials are enclosed in some annular sectors that take into account the magnitude of the coefficients. Following Kennedy and Dehmer, we provide the zero inclusion regions of all the zeros of complex-valued harmonic polynomials in general, and in particular, we bound all the zeros of some families of harmonic trinomials in a certain annular region.

Suggested Citation

  • Hunduma Legesse Geleta & Oluma Ararso Alemu & Firdous A. Shah, 2022. "Location of the Zeros of Certain Complex-Valued Harmonic Polynomials," Journal of Mathematics, Hindawi, vol. 2022, pages 1-5, August.
    • Handle: RePEc:hin:jjmath:4886522
    DOI: 10.1155/2022/4886522
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    Cited by:

    1. Jennifer Brooks & Megan Dixon & Michael Dorff & Alexander Lee & Rebekah Ottinger, 2023. "Zeros of Convex Combinations of Elementary Families of Harmonic Functions," Mathematics, MDPI, vol. 11(19), pages 1-14, September.

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