Cécile Dartyge

activity

20182022

collaborators

3 papers

math.NT2022

On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases

Cécile Dartyge, James Maynard

Let $P (X) \in Z [X]$ be an irreducible, monic, quartic polynomial with cyclic or dihedral Galois group. We prove that there exists a constant $c_{P} > 0$ such that for a positive…

math.NT2020

On the distribution of the Rudin-Shapiro function for finite fields

Cécile Dartyge, László Mérai, Arne Winterhof

Let $q = p^{r}$ be the power of a prime $p$ and $(β_{1}, \dots, β_{r})$ be an ordered basis of $F_{q}$ over $F_{p}$ . For $$ ξ=\sum\limits_{j=1}^r x_jβ_j\in \mathbb{F}_q \quad…

math.NT2018

Exponential sums with reducible polynomials

Cécile Dartyge, Greg Martin

Hooley proved that if $f \in Z [X]$ is irreducible of degree $\geq 2$ , then the fractions ${r / n}$ , $0 < r < n$ with $f (r) \equiv 0 (mod n)$ , are uniformly distributed in $(0, 1)$ . I…