Abstract
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.
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The author thanks for the suggestions given by the reviewer, which have improved the final version of this article.
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This research was supported by the Science & Engineering Research Board (SERB), Department of Science & Technology, Government of India (No. MTR/2022/000118).
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Mir, A. On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem. Czech Math J 73, 649–662 (2023). https://doi.org/10.21136/CMJ.2023.0097-22
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DOI: https://doi.org/10.21136/CMJ.2023.0097-22