2 research outputs found
Egerv\'ary's theorems for harmonic trinomials
In this manuscript, we study the arrangements of the roots in the complex
plane for the lacunary harmonic polynomials called harmonic trinomials. We
provide necessary and sufficient conditions so that two general harmonic
trinomials have the same set of roots up to a rotation around the origin in the
complex plane, a reflection over the real axis, or a composition of the
previous both transformations. This extends the results of J. Egerv\'ary 1930
for the setting of trinomials to the setting of harmonic trinomials.Comment: 17 page