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arXiv · 2211.16554

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

Oluma Ararso Alemu·Hunduma Legesse Geleta
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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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Oluma Ararso Alemu, Hunduma Legesse Geleta. 2022-11-29. The Image of Critical Circle and Zero-free Curve for Quadrinomials. https://arxiv.org/abs/2211.16554

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