A note on monogenic even polynomials
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913839142928384 |
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| author | König, Joachim |
| author_facet | König, Joachim |
| contents | We extend several predecessor works on even sextic monogenic polynomials. In particular, we prove a conjecture of Lenny Jones, thereby classifying even sextic monogenic polynomials with cyclic Galois group. This result is key to completing previous partial results on existence or non-existence of infinite families of even sextic monogenic polynomials with a prescribed Galois group. Some of the underlying ideas are relevant for investigation of more general families of even polynomials $f(X^2)$, or power-compositional polynomials $f(X^\ell)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on monogenic even polynomials König, Joachim Number Theory We extend several predecessor works on even sextic monogenic polynomials. In particular, we prove a conjecture of Lenny Jones, thereby classifying even sextic monogenic polynomials with cyclic Galois group. This result is key to completing previous partial results on existence or non-existence of infinite families of even sextic monogenic polynomials with a prescribed Galois group. Some of the underlying ideas are relevant for investigation of more general families of even polynomials $f(X^2)$, or power-compositional polynomials $f(X^\ell)$. |
| title | A note on monogenic even polynomials |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.10119 |