Irreducible Polynomials with Coefficients in an Affine Algebraic Set
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915664618323968 |
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| author | Kolekar, Neil |
| author_facet | Kolekar, Neil |
| contents | In this paper, we give error bounds on the number of monic irreducible polynomials $a_0+a_1x+\dots+a_{n-1}x^{n-1}+x^n$ over a finite field $\mathbb{F}_q$ of degree $n$ with $(a_0, a_1, \dots, a_{n-1}, 1)$ lying in a fixed affine algebraic set $V$ of points in $\mathbb{F}_q^{n+1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible Polynomials with Coefficients in an Affine Algebraic Set Kolekar, Neil Number Theory In this paper, we give error bounds on the number of monic irreducible polynomials $a_0+a_1x+\dots+a_{n-1}x^{n-1}+x^n$ over a finite field $\mathbb{F}_q$ of degree $n$ with $(a_0, a_1, \dots, a_{n-1}, 1)$ lying in a fixed affine algebraic set $V$ of points in $\mathbb{F}_q^{n+1}$. |
| title | Irreducible Polynomials with Coefficients in an Affine Algebraic Set |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.08994 |