Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915058980749312 |
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| author | Hazarika, Himangshu Kapetanakis, Giorgos Basnet, Dhiren Kumar |
| author_facet | Hazarika, Himangshu Kapetanakis, Giorgos Basnet, Dhiren Kumar |
| contents | Let $\Fm$ be finite fields of order $q^m$, where $m\geq 2$ and $q$, a prime power. Given $\F$-affine hyperplanes $A_1,\ldots, A_m$ of $\Fm$ in general position, we study the existence of primitive element $α$ of $\Fm$, such that $f(α)$ is also primitive, where $ax^2+bx+c\in \Fm[x]$ ($a\neq 0$ and $b^2\neq 4ac$) in $\Fm$ and the primitive pair $(α, f(α))$ avoids each $A_i$. We establish results for fields of higher order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes Hazarika, Himangshu Kapetanakis, Giorgos Basnet, Dhiren Kumar Number Theory 12E20, 11T23 Let $\Fm$ be finite fields of order $q^m$, where $m\geq 2$ and $q$, a prime power. Given $\F$-affine hyperplanes $A_1,\ldots, A_m$ of $\Fm$ in general position, we study the existence of primitive element $α$ of $\Fm$, such that $f(α)$ is also primitive, where $ax^2+bx+c\in \Fm[x]$ ($a\neq 0$ and $b^2\neq 4ac$) in $\Fm$ and the primitive pair $(α, f(α))$ avoids each $A_i$. We establish results for fields of higher order. |
| title | Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes |
| topic | Number Theory 12E20, 11T23 |
| url | https://arxiv.org/abs/2412.08455 |