Binary forms with the same value set II. The case of ${\bf D}_4$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911848332263424 |
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| author | Fouvry, Étienne Koymans, Peter |
| author_facet | Fouvry, Étienne Koymans, Peter |
| contents | Let $F, G \in \mathbb{Z}[X, Y]$ be binary forms of degree $\geq 3$, non-zero discriminant and with automorphism group isomorphic to $D_4$. If $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$, we show that $F$ and $G$ are ${\rm GL}(2, \mathbb{Z})$--equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Binary forms with the same value set II. The case of ${\bf D}_4$ Fouvry, Étienne Koymans, Peter Number Theory Let $F, G \in \mathbb{Z}[X, Y]$ be binary forms of degree $\geq 3$, non-zero discriminant and with automorphism group isomorphic to $D_4$. If $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$, we show that $F$ and $G$ are ${\rm GL}(2, \mathbb{Z})$--equivalent. |
| title | Binary forms with the same value set II. The case of ${\bf D}_4$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.13952 |