Binary forms with the same value set III. The case of ${\bf D}_3$ and ${\bf D_6}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909184112459776 |
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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 $\geq 3$ with automorphism groups isomorphic to the dihedral group of cardinality $6$ or $12$. We characterize exactly when $F$ and $G$ have the same value set, i.e. $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Binary forms with the same value set III. The case of ${\bf D}_3$ and ${\bf D_6}$ Fouvry, Étienne Koymans, Peter Number Theory Let $F, G \in \mathbb{Z}[X, Y]$ be binary forms of degree $\geq 3$ with automorphism groups isomorphic to the dihedral group of cardinality $6$ or $12$. We characterize exactly when $F$ and $G$ have the same value set, i.e. $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$. |
| title | Binary forms with the same value set III. The case of ${\bf D}_3$ and ${\bf D_6}$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.18725 |