On the Eneström–Kakeya theorem for quaternionic polynomials

Abdullah Mir; Abrar Ahmad

doi:10.5802/crmath.467

Complex analysis and geometry

On the Eneström–Kakeya theorem for quaternionic polynomials

Abdullah Mir ¹ ; Abrar Ahmad ¹

¹ Department of Mathematics, University of Kashmir, Srinagar, 190006, India

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1051-1062.

Abstract

In this paper, we present certain results concerning the distribution of zeros of polynomials of a quaternionic variable and with quaternionic coefficients. We obtain ring shaped regions of Eneström–Kakeya type for the zeros of these polynomials and also extend some classical results from the complex to quaternionic setting.

Received: 2022-02-26
Revised: 2022-11-11
Accepted: 2023-01-25
Published online: 2023-09-07

DOI: 10.5802/crmath.467

Classification: 30E10, 30G35, 16K20

Author's affiliations:

Abdullah Mir ¹; Abrar Ahmad ¹

¹ Department of Mathematics, University of Kashmir, Srinagar, 190006, India

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Abdullah Mir and Abrar Ahmad},
     title = {On the {Enestr\"om{\textendash}Kakeya} theorem for quaternionic polynomials},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1051--1062},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.467},
     language = {en},
}

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Abdullah Mir; Abrar Ahmad. On the Eneström–Kakeya theorem for quaternionic polynomials. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1051-1062. doi : 10.5802/crmath.467. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.467/

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