Michel Waldschmidt

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20232026

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math.NT2026

On the convexity of the fundamental domain of binary cyclotomic forms

Étienne Fouvry, Michel Waldschmidt

Denote by $Φ_{m} (X, Y) \in Z [X, Y]$ , $m ⩾ 1$ the sequence of binary cyclotomic forms, so that $Φ_{m} (T, 1) \in Z [T]$ , $m ⩾ 1$ is the sequence of cyclotomic polynomials. We pro…

math.NT2025

Number of integers represented by families of binary forms III: fewnomials

Etienne Fouvry, Michel Waldschmidt

In a series of papers we investigated the following question: given a family $\calF$ of binary forms having nonzero discriminant and integer coefficients, for each $d ⩾ 3$ ,…

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…