On the number of roots for harmonic trinomials

Abstract

In this manuscript we study the counting problem for harmonic trinomials of the form $a{\zeta }^n+b{\overline{\zeta }}^m+c$, where $n,m\in \mathbb{N}$, $n>m$, and $a$, $b$ and $c$ are non-zero complex numbers. As a consequence, we obtain the Fundamental Theorem of Algebra and the Wilmshurst conjecture for harmonic trinomials. The proof of the counting problem relies on the Bohl method introduced in Bohl (1908).

arXiv comment14 pages

Cited by in corpus (1)

• Egerváry's theorems for harmonic trinomials