English

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

Number Theory 2024-04-30 v1

Abstract

Let F,GZ[X,Y]F, G \in \mathbb{Z}[X, Y] be binary forms of degree 3\geq 3 with automorphism groups isomorphic to the dihedral group of cardinality 66 or 1212. We characterize exactly when FF and GG have the same value set, i.e. F(Z2)=G(Z2)F(\mathbb{Z}^2) = G(\mathbb{Z}^2).

Cite

@article{arxiv.2404.18725,
  title  = {Binary forms with the same value set III. The case of ${\bf D}_3$ and ${\bf D_6}$},
  author = {Étienne Fouvry and Peter Koymans},
  journal= {arXiv preprint arXiv:2404.18725},
  year   = {2024}
}
R2 v1 2026-06-28T16:09:50.423Z