On the Theorem of Gauss--Lucas for quaternions
Classical Analysis and ODEs
2026-03-03 v2 Rings and Algebras
Abstract
It is proved that the roots of the derivative of a polynomial with quaternionic coefficients belong to the union of the intersections of sets defined in terms of certain projections of a polynomial. The result strengthens the quaternion version of Gauss-Lucas theorem, proved by Ghiloni and Perotti in 2018.
Cite
@article{arxiv.2510.22433,
title = {On the Theorem of Gauss--Lucas for quaternions},
author = {I. Emizh and A. Guterman},
journal= {arXiv preprint arXiv:2510.22433},
year = {2026}
}