Binary forms with the same value set III. The case of D3 and D6

Abstract

Let $F,G\in Z[X,Y]$ be binary forms of degree ≥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. $F\left(Z^2\right)=G\left(Z^2\right)$.