Zeros of a one-parameter family of harmonic trinomials

Brilleslyper, Michael; Brooks, Jennifer; Dorff, Michael; Howell, Russell; Schaubroeck, Lisbeth

doi:10.1090/bproc/51

Zeros of a one-parameter family of harmonic trinomials
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by Michael Brilleslyper, Jennifer Brooks, Michael Dorff, Russell Howell and Lisbeth Schaubroeck HTML | PDF

Proc. Amer. Math. Soc. Ser. B 7 (2020), 82-90

Abstract:

It is well known that complex harmonic polynomials of degree $n$ may have more than $n$ zeros. In this paper, we examine a one-parameter family of harmonic trinomials and determine how the number of zeros depends on the parameter. Our proof heavily utilizes the Argument Principle for Harmonic Functions and involves finding the winding numbers about the origin for a family of hypocycloids.

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