On the Theorem of Gauss--Lucas for quaternions
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914360715116544 |
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| author | Emizh, I. Guterman, A. |
| author_facet | Emizh, I. Guterman, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Theorem of Gauss--Lucas for quaternions Emizh, I. Guterman, A. Classical Analysis and ODEs Rings and Algebras 30C15, 30G35, 32A30 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. |
| title | On the Theorem of Gauss--Lucas for quaternions |
| topic | Classical Analysis and ODEs Rings and Algebras 30C15, 30G35, 32A30 |
| url | https://arxiv.org/abs/2510.22433 |