English

Zeros of harmonic polynomials, critical lemniscates and caustics

Complex Variables 2016-01-21 v2

Abstract

In this paper we sharpen significantly several known estimates on the maximal number of zeros of complex harmonic polynomials. We also study the relation between the curvature of critical lemniscates and its impact on geometry of caustics and the number of zeros of harmonic polynomials.

Keywords

Cite

@article{arxiv.1508.04439,
  title  = {Zeros of harmonic polynomials, critical lemniscates and caustics},
  author = {Dmitry Khavinson and Seung-Yeop Lee and Andres Saez},
  journal= {arXiv preprint arXiv:1508.04439},
  year   = {2016}
}

Comments

18 pages, 7 figures, Theorem 1 corrected and a remark added