Zeros of a one-parameter family of harmonic trinomials

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

Reference18 articles.

1. Locating unimodular roots;Brilleslyper, Michael A.;College Math. J.,2014

2. Counting interior roots of trinomials;Brilleslyper, Michael A.;Math. Mag.,2018

3. The exact bound on the number of zeros of harmonic polynomials;Bshouty, Daoud;J. Anal. Math.,1995

4. Harmonic univalent functions;Clunie, J.;Ann. Acad. Sci. Fenn. Ser. A I Math.,1984

5. Anamorphosis, mapping problems, and harmonic univalent functions;Dorff, Michael J.,2012

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Corrigendum to “On the number of roots for harmonic trinomials” [J. Math. Anal. Appl. 514 (2) (2022) 126313];Journal of Mathematical Analysis and Applications;2024-07

2. Egerváry's theorems for harmonic trinomials;Acta Mathematica Hungarica;2024-02

3. Zeros of Convex Combinations of Elementary Families of Harmonic Functions;Mathematics;2023-09-25

4. Location of the Zeros of Harmonic Trinomials;Bulletin of the Malaysian Mathematical Sciences Society;2022-11-29

5. On the number of roots for harmonic trinomials;Journal of Mathematical Analysis and Applications;2022-10

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3