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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.08618 |
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| _version_ | 1866917951711477760 |
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| author | Tripathi, D. |
| author_facet | Tripathi, D. |
| contents | {In 2020, Carney et.al. proved the quaternionic version of the Eneström-Kakeya Theorem, which states that a polynomial $p(q)=\sum_{ν=0}^n q^νa_ν$ with non-negative and monotonically increasing coefficients $(0<a_0\le a_1\le \cdots \le a_n)$ has all of its zeros within the unit ball $|q|\le 1$. Numerous generalizations of Eneström-Kakeya Theorem are available in the literatures (\cite{m}-\cite{mmr}). In this paper, we extend some of these generalizations to the quaternionic context and present several potential results.} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternionic Generalization of the Eneström-Kakeya Theorem Tripathi, D. Complex Variables 30G35, 16K20, 30E10 {In 2020, Carney et.al. proved the quaternionic version of the Eneström-Kakeya Theorem, which states that a polynomial $p(q)=\sum_{ν=0}^n q^νa_ν$ with non-negative and monotonically increasing coefficients $(0<a_0\le a_1\le \cdots \le a_n)$ has all of its zeros within the unit ball $|q|\le 1$. Numerous generalizations of Eneström-Kakeya Theorem are available in the literatures (\cite{m}-\cite{mmr}). In this paper, we extend some of these generalizations to the quaternionic context and present several potential results.} |
| title | Quaternionic Generalization of the Eneström-Kakeya Theorem |
| topic | Complex Variables 30G35, 16K20, 30E10 |
| url | https://arxiv.org/abs/2503.08618 |