$2$-superirreducibility of univariate polynomials over $\mathbb{Q}$ and $\mathbb{Z}$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911007939493888 |
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| author | Du, Lara |
| author_facet | Du, Lara |
| contents | This paper investigates whether or not polynomials that are irreducible over $\mathbb{Q}$ and $\mathbb{Z}$ can remain irreducible under substitution by all quadratic polynomials. It answers this question in the negative in the degree 2 and 3 cases and provides families of examples in both the affirmative and the negative categories in the degree 4 case. Finally this paper explores what happens in higher degree cases, providing a family of examples in the negative category and offering a conjectured family for the positive category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $2$-superirreducibility of univariate polynomials over $\mathbb{Q}$ and $\mathbb{Z}$ Du, Lara Number Theory This paper investigates whether or not polynomials that are irreducible over $\mathbb{Q}$ and $\mathbb{Z}$ can remain irreducible under substitution by all quadratic polynomials. It answers this question in the negative in the degree 2 and 3 cases and provides families of examples in both the affirmative and the negative categories in the degree 4 case. Finally this paper explores what happens in higher degree cases, providing a family of examples in the negative category and offering a conjectured family for the positive category. |
| title | $2$-superirreducibility of univariate polynomials over $\mathbb{Q}$ and $\mathbb{Z}$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.16206 |