Zeros of harmonic polynomials with complex coefficients
Volume 168 / 2022
Colloquium Mathematicum 168 (2022), 119-126
MSC: 30C10, 30C15, 42A50.
DOI: 10.4064/cm7874-4-2021
Published online: 15 November 2021
Abstract
We study the maximal number of zeros of harmonic polynomials with complex coefficients. We also study the zeros of harmonic polynomials with complex coefficients which admit a decomposition $F(z)=P_{n}(z)+\overline {Q_{m}(z)}$ where $P_{n}$ and $Q_{m}$ are polynomials of degree $n$ and $m$ (respectively), with $n \gt m$.
