Zobrazeno 1 - 10
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pro vyhledávání: '"Fouvry, Étienne"'
Autor:
Fouvry, Étienne, Koymans, Peter
Let $F, G \in \mathbb{Z}[X, Y]$ be binary forms of degree $\geq 3$ with automorphism groups isomorphic to the dihedral group of cardinality $6$ or $12$. We characterize exactly when $F$ and $G$ have the same value set, i.e. $F(\mathbb{Z}^2) = G(\math
Externí odkaz:
http://arxiv.org/abs/2404.18725
Autor:
Fouvry, Étienne, Koymans, Peter
Let $F, G \in \mathbb{Z}[X, Y]$ be binary forms of degree $\geq 3$, non-zero discriminant and with automorphism group isomorphic to $D_4$. If $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$, we show that $F$ and $G$ are ${\rm GL}(2, \mathbb{Z})$--equivalent.
Externí odkaz:
http://arxiv.org/abs/2404.13952
Autor:
Fouvry, Étienne, Koymans, Peter
Given a binary form $F \in \mathbb{Z}[X, Y]$, we define its value set to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. Let $F, G \in \mathbb{Z}[X, Y]$ be two binary forms of degree $d \geq 3$ and with non-zero discriminant. In a series of three papers,
Externí odkaz:
http://arxiv.org/abs/2404.11231
Autor:
Fouvry, Étienne, Koymans, Peter
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
Externí odkaz:
http://arxiv.org/abs/2404.09575
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between Farey fra
Externí odkaz:
http://arxiv.org/abs/2404.09295
Autor:
Fouvry, Étienne, Waldschmidt, Michel
We consider some families of binary binomial forms $aX^d+bY^d$, with $a$ and $b$ integers. Under suitable assumptions, we prove that every rational integer $m$ with $|m|\ge 2$ is only represented by a finite number of the forms of this family (with v
Externí odkaz:
http://arxiv.org/abs/2306.02462
We initiate the study of certain families of $L$-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values $L(\demi,\chi^a)L(\demi,\chi^b)$ for a
Externí odkaz:
http://arxiv.org/abs/2303.11664
Autor:
Fouvry, Étienne, Shparlinski, Igor E.
We estimate weighted character sums with determinants $ad-bc $ of $2\times 2$ matrices modulo a prime $p$ with entries $a,b,c,d $ varying over the interval $ [1,N]$. Our goal is to obtain nontrivial bounds for values of $N$ as small as possible. In p
Externí odkaz:
http://arxiv.org/abs/2210.15761
Autor:
Fouvry, Étienne, Waldschmidt, Michel
We extend our previous results on the number of integers which are values of some cyclotomic form of degree larger than a given value (see \cite{FW1}), to more general families of binary forms with integer coefficients. Our main ingredient is an asym
Externí odkaz:
http://arxiv.org/abs/2206.03733
Autor:
Fouvry, Étienne, Koymans, Peter
We prove Malle's conjecture for nonic Heisenberg extensions over $\mathbb{Q}$. Our main algebraic result shows that the number of nonic Heisenberg extensions over $\mathbb{Q}$ with discriminant bounded by $X$ is given by a character sum. We then extr
Externí odkaz:
http://arxiv.org/abs/2102.09465