Critical Curve and Singular Zeros of Harmonic Quadrinomial
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Date
2024-10
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Addis Ababa University
Abstract
In this thesis, we show that the critical curve of the quadrinomial Pb(z) = bzk + 1
k1 zk1 +
1
n zn + kb
n1 zn1 is the part of the unit circle. Moreover, we prove that there are at most two
singular zeros for the quadrinomial Pb(z) = bzk+ 1
k1 zk1+ 1
n zn+ kb
n1 zn1 we are considering.
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Keywords
Analytic Functions, Harmonic Polynomials, Harmonic Quadrinomials, Sense Preserving, Sense Reversing, Critical Curves, Zeros, Singular, and Nonsingular Zeros