Density of Special Classes of Polynomials with Squarefree Discriminant
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909607288373248 |
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| author | Sanjaya, Gian Cordana |
| author_facet | Sanjaya, Gian Cordana |
| contents | In this paper, we consider the problem of determining the density of monic polynomials over $\mathbb{Z}_p$ with squarefree discriminant over various subsets of the set of monic polynomials over $\mathbb{Z}_p$ of fixed degree. We compute the density of polynomials in each subset whose discriminant is squarefree, and we compute the density of polynomials $f$ in each subset such that $\mathbb{Z}_p[x]/(f(x))$ is the maximal order of $\mathbb{Q}_p[x]/(f(x))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density of Special Classes of Polynomials with Squarefree Discriminant Sanjaya, Gian Cordana Number Theory 11N32, 11N36, 11T06 In this paper, we consider the problem of determining the density of monic polynomials over $\mathbb{Z}_p$ with squarefree discriminant over various subsets of the set of monic polynomials over $\mathbb{Z}_p$ of fixed degree. We compute the density of polynomials in each subset whose discriminant is squarefree, and we compute the density of polynomials $f$ in each subset such that $\mathbb{Z}_p[x]/(f(x))$ is the maximal order of $\mathbb{Q}_p[x]/(f(x))$. |
| title | Density of Special Classes of Polynomials with Squarefree Discriminant |
| topic | Number Theory 11N32, 11N36, 11T06 |
| url | https://arxiv.org/abs/2505.06820 |