Egerváry's theorems for harmonic trinomials
摘要
We study the arrangements of the roots in the complex planefor the lacunary harmonic polynomials called harmonic trinomials. We providenecessary and sufficient conditions so that two general harmonic trinomials havethe same set of roots up to a rotation around the origin in the complex plane, areflection over the real axis, or a composition of the previous both transformations.This extends the results of Jenő Egerváry given in [19] for the setting oftrinomials to the setting of harmonic trinomials.