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arXiv · 2404.13952

Binary forms with the same value set II. The case of ${\bf D}_4$

Étienne Fouvry·Peter Koymans
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Abstract

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.

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Étienne Fouvry, Peter Koymans. 2024-04-22. Binary forms with the same value set II. The case of ${\bf D}_4$. https://arxiv.org/abs/2404.13952

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