The Image of Critical Circle and Zero-free Curve for Quadrinomials

2022/11/29 by Oluma Ararso Alemu, Alemu, Oluma Ararso, Hunduma Legesse Geleta +1 · 1 citation
Engineering · Mathematics · #30A05 #Advanced Numerical Analysis Techniques #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2211.16554

openalex publication_date 2022/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The location of the zeros of a two-parameter family of complex-valued harmonic quadrinomials depends on the parameters. In this paper, we determine and demonstrate that the image of some critical circle under these two-parameter family of complex-valued harmonic quadrinomial is a hypocycloid. We also determine a zero-free curve for two-parameter family of quadratic qudrinomial.

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