Zeros of a one-parameter family of harmonic trinomials-Reference-Cited by-同舟云学术

Zeros of a one-parameter family of harmonic trinomials

Published:2020-06-17 Issue:7 Volume:7 Page:82-90
ISSN:2330-1511
Container-title:Proceedings of the American Mathematical Society, Series B
language:en
Short-container-title:Proc. Amer. Math. Soc. Ser. B

Author:

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

Abstract

It is well known that complex harmonic polynomials of degree n n may have more than n 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.

Publisher

American Mathematical Society (AMS)

Subject

General Medicine

Link

https://www.ams.org/bproc/2020-07-07/S2330-1511-2020-00051-7/S2330-1511-2020-00051-7.pdf

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