English

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.

Keywords

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}
}