Pierre-Yves Bienvenu

activity

20172026

most citedOn the density or measure of sets and their sumsets in the integers or the circle

9 citations · 11 across the 9 of their papers we have counts for

collaborators

12 papers

math.NT2026

A Generalization of Sárközy's theorem in function fields

Pierre-Yves Bienvenu, Thái Hoàng Lê, Gauree Wathodkar

Sárközy's theorem says that if $A \subset Z$ has positive upper asymptotic density, then there are distinct $a_{1}, a_{2} \in A$ and $n \in Z$ such that $a_1-a_2 = n^…

math.NT2026

Additive index and Carlitz rank

Pierre-Yves Bienvenu, Arne Winterhof

We compare several complexity measures for self-mappings of finite fields. In particular, we show that Carlitz rank and additive index cannot be small simultaneously up to trivial…

math.DS2026

Bohr sets in sumsets III: expanding difference sets and almost Bohr sets

Pierre-Yves Bienvenu, John T. Griesmer, Anh N. Le +1

Let $G$ be a discrete abelian group. Følner showed that if $A \subseteq G$ has positive upper Banach density, then $A - A$ contains an almost Bohr set -- a set of the form $B \setm…

math.NT2026

On the additive index of the Diffie-Hellman mapping and the discrete logarithm

Pierre-Yves Bienvenu, Arne Winterhof

Several complexity measures such as degree, sparsity and multiplicative index for cryptographic functions including the Diffie-Hellman mapping and the discrete logarithm in a finit…

math.NT2025

Realisability of simultaneous density constraints for sets of integers

Pierre-Yves Bienvenu

In this note, we study the set $D$ of values of the quadruplet $(d (A), d (A), d (2 A), d (2 A))$ …

math.NT2024

Intersective sets for sparse sets of integers

Pierre-Yves Bienvenu, John T. Griesmer, Anh N. Le +1

For $E \subset N$ , a subset $R \subset N$ is $E$ -intersective if for every $A \subset E$ having positive upper relative density, we have $R \cap (A - A) \neq \var…