Zero Distribution of Polynomials Generated by a Power of a Cubic Polynomial
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916712386920448 |
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| author | Steele, Travis Tran, Khang |
| author_facet | Steele, Travis Tran, Khang |
| contents | For each $α>0$ and $A(z),B(z)\in\mathbb{C}[z]$, we study the zero distribution of the sequence of polynomials $\left\{ P_{m}^{(α)}(z)\right\} _{m=0}^{\infty}$ generated by $(1+B(z)t+A(z)t^{3})^{-α}$. We show that for large $m$, the zeros of $P_{m}^{(α)}(z)$ lie on an explicit curve on the complex plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zero Distribution of Polynomials Generated by a Power of a Cubic Polynomial Steele, Travis Tran, Khang Complex Variables 30C15, 26C10, 11C08 For each $α>0$ and $A(z),B(z)\in\mathbb{C}[z]$, we study the zero distribution of the sequence of polynomials $\left\{ P_{m}^{(α)}(z)\right\} _{m=0}^{\infty}$ generated by $(1+B(z)t+A(z)t^{3})^{-α}$. We show that for large $m$, the zeros of $P_{m}^{(α)}(z)$ lie on an explicit curve on the complex plane. |
| title | Zero Distribution of Polynomials Generated by a Power of a Cubic Polynomial |
| topic | Complex Variables 30C15, 26C10, 11C08 |
| url | https://arxiv.org/abs/2504.20374 |