Étienne Fouvry

most citedBinary forms with the same value set I

1 citations · 1 across the 5 of their papers we have counts for

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5 papers

math.NT2024

Binary forms with the same value set III. The case of $D_{3}$ and $D_{6}$

Étienne Fouvry, Peter Koymans

Let $F, G \in Z [X, Y]$ be binary forms of degree $\geq 3$ with automorphism groups isomorphic to the dihedral group of cardinality $6$ or $12$ . We characterize exactly whe…

math.NT2024

Binary quadratic forms with the same value set

Étienne Fouvry, Peter Koymans

Given a binary quadratic form $F \in Z [X, Y]$ , we define its value set $F (Z^{2})$ to be ${F (x, y) : (x, y) \in Z^{2}}$ . If $F$ and $G$ are two binary quadr…

math.NT2024

Binary forms with the same value set II. The case of $D_{4}$

Étienne Fouvry, Peter Koymans

Let $F, G \in Z [X, Y]$ be binary forms of degree $\geq 3$ , non-zero discriminant and with automorphism group isomorphic to $D_{4}$ . If $F (Z^{2}) = G (Z^{2})$ , w…

math.NT2024★ 1 cited

Binary forms with the same value set I

Étienne Fouvry, Peter Koymans

Given a binary form $F \in Z [X, Y]$ , we define its value set to be ${F (x, y) : (x, y) \in Z^{2}}$ . Let $F, G \in Z [X, Y]$ be two binary forms of degree $…

math.NT2023

Number of integers represented by families of binary forms II: binomial forms

Étienne Fouvry, Michel Waldschmidt

We consider some families of binary binomial forms $a X^{d} + b Y^{d}$ , with $a$ and $b$ integers. Under suitable assumptions, we prove that every rational integer $m$ with $∣ m ∣ \geq 2$ is o…

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

Binary quadratic forms with the same value set

Binary forms with the same value set II. The case of D4​

Binary forms with the same value set I

Number of integers represented by families of binary forms II: binomial forms

Binary forms with the same value set III. The case of $D_{3}$ and $D_{6}$

Binary forms with the same value set II. The case of $D_{4}$