Geodesic
On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 649-662
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We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.
DOI : 10.21136/CMJ.2023.0097-22
Classification : 16K20, 30E10, 30G35
Keywords: quaternionic polynomial; Eneström-Kakeya theorem; zero-sets of a regular product 
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Mir, Abdullah. On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 649-662. doi: 10.21136/CMJ.2023.0097-22

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