调和多项式的零点，临界双纽线和焦散线
Zeros of harmonic polynomials, critical lemniscates and caustics
摘要：
在本文中，我们显着锐化几个已知的估计的最大零点数的复调和多项式。我们还研究了临界双纽线的曲率与焦散线几何和调和多项式零点个数的关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
