Squarefree discriminants of polynomials with prime coefficients
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866929687620485120 |
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| author | Iverson, Valentio Sanjaya, Gian Cordana Wang, Xiaoheng |
| author_facet | Iverson, Valentio Sanjaya, Gian Cordana Wang, Xiaoheng |
| contents | In this paper, we consider the family of monic polynomials with prime coefficients and the family of all polynomials with prime coefficients. We determine the number of $f(x)$ in each of these families having: squarefree discriminant; $\mathbb{Z}[x]/(f(x))$ as the maximal order in $\mathbb{Q}[x]/(f(x))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Squarefree discriminants of polynomials with prime coefficients Iverson, Valentio Sanjaya, Gian Cordana Wang, Xiaoheng Number Theory 11N32, 11N36, 11T06 In this paper, we consider the family of monic polynomials with prime coefficients and the family of all polynomials with prime coefficients. We determine the number of $f(x)$ in each of these families having: squarefree discriminant; $\mathbb{Z}[x]/(f(x))$ as the maximal order in $\mathbb{Q}[x]/(f(x))$. |
| title | Squarefree discriminants of polynomials with prime coefficients |
| topic | Number Theory 11N32, 11N36, 11T06 |
| url | https://arxiv.org/abs/2501.09697 |