Binary forms with the same value set III. The case of ${\bf D}_3$ and ${\bf D_6}$

Étienne Fouvry; Peter Koymans

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arXiv · 2404.18725

Binary forms with the same value set III. The case of ${\bf D}_3$ and ${\bf D_6}$

Étienne Fouvry·Peter Koymans

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Abstract

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. $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$.

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Étienne Fouvry, Peter Koymans. 2024-04-29. Binary forms with the same value set III. The case of ${\bf D}_3$ and ${\bf D_6}$. https://arxiv.org/abs/2404.18725

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