Factorization type probabilities of polynomials with prescribed coefficients over a finite field
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866916267828445184 |
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| author | Slavov, Kaloyan |
| author_facet | Slavov, Kaloyan |
| contents | Let $f(T)$ be a monic polynomial of degree $d$ with coefficients in a finite field $\mathbb{F}_q$. Extending earlier results in the literature, but now allowing $(q,2d)>1$, we give a criterion for $f$ to satisfy the following property: for all but $d^2-d-1$ values of $s$ in $\mathbb{F}_q$, the probability that $f(T)+sT+b$ is irreducible over $\mathbb{F}_q$ (as $b\in\mathbb{F}_q$ is chosen uniformly at random) is $1/d+O(q^{-1/2})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_09050 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Factorization type probabilities of polynomials with prescribed coefficients over a finite field Slavov, Kaloyan Algebraic Geometry 14G15, 12F10 Let $f(T)$ be a monic polynomial of degree $d$ with coefficients in a finite field $\mathbb{F}_q$. Extending earlier results in the literature, but now allowing $(q,2d)>1$, we give a criterion for $f$ to satisfy the following property: for all but $d^2-d-1$ values of $s$ in $\mathbb{F}_q$, the probability that $f(T)+sT+b$ is irreducible over $\mathbb{F}_q$ (as $b\in\mathbb{F}_q$ is chosen uniformly at random) is $1/d+O(q^{-1/2})$. |
| title | Factorization type probabilities of polynomials with prescribed coefficients over a finite field |
| topic | Algebraic Geometry 14G15, 12F10 |
| url | https://arxiv.org/abs/1903.09050 |