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Binary quadratic forms with the same value set
Published 15 Apr 2024 in math.NT | (2404.09575v2)
Abstract: Given a binary quadratic form $F \in \mathbb{Z}[X, Y]$, we define its value set $F(\mathbb{Z}2)$ to be ${F(x, y) : (x, y) \in \mathbb{Z}2}$. If $F$ and $G$ are two binary quadratic forms with integer coefficients, we give necessary and sufficient conditions on $F$ and $G$ for $F(\mathbb{Z}2) = G(\mathbb{Z}2)$.
- É. Fouvry and P. Koymans, Binary forms with the same value set I. In preparation.
- É. Fouvry and P. Koymans, Binary forms with the same value set II. The case of 𝐃4subscript𝐃4{\bf D}_{4}bold_D start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT. In preparation.
- É. Fouvry and P. Koymans, Binary forms with the same value set III. The case of 𝐃3subscript𝐃3{\bf D}_{3}bold_D start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT and 𝐃6subscript𝐃6{\bf D}_{6}bold_D start_POSTSUBSCRIPT 6 end_POSTSUBSCRIPT. In preparation.
- G.S. Kopp and J.C. Lagarias, Class field theory for orders of number fields. arXiv preprint: 2212.09177.
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