Pierre-Yves Bienvenu

activity

20152026

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

9 citations · 16 across the 14 of their papers we have counts for

collaborators

19 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…

math.NT2022★ 2 cited

On algebraic properties of power monoids of numerical monoids

Pierre-Yves Bienvenu, Alfred Geroldinger

Let $S \subset N_{0}$ be a numerical monoid and let $P_{fin} (S)$ , resp $P_{fin, 0} (S)$ , denote the power monoid, resp. the restricted pow…

math.NT2022

Metric decomposability theorems on sets of integers

P. -Y. Bienvenu

A set $A \subset N$ is called additively decomposable (resp. asymptotically additively decomposable) if there exist sets $\mathcal{B},\mathcal{C}\subset \mathbb{N…

math.NT2021★ 1 cited

A transference principle for systems of linear equations, and applications to almost twin primes

Pierre-Yves Bienvenu, Xuancheng Shao, Joni Teräväinen

The transference principle of Green and Tao enabled various authors to transfer Szemerédi's theorem on long arithmetic progressions in dense sets to various sparse sets of integers…

math.CO2020★ 1 cited

On additive bases in infinite abelian semigroups

Pierre-Yves Bienvenu, Benjamin Girard, Thái Hoàng Lê

Building on previous work by Lambert, Plagne and the third author, we study various aspects of the behavior of additive bases in infinite abelian groups and semigroups. We show tha…

math.NT2019

Kneser's Theorem in $σ$ -finite Abelian groups

Pierre-Yves Bienvenu, François Hennecart

Let $G$ be a $σ$ -finite abelian group, i.e. $G = ⋃_{n \geq 1} G_{n}$ where $(G_{n})_{n \geq 1}$ is a non decreasing sequence of finite subgroups. For any $A \subset G$ , let $\underlin…

math.NT2019★ 9 cited

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

Pierre-Yves Bienvenu, François Hennecart

Let $d (A)$ be the asymptotic density (if it exists) of a sequence of integers $A$ . For any real numbers $0 \leq α \leq β \leq 1$ , we solve the question of the existence of a se…

math.NT2018★ 2 cited

A note on the set $A (A + A)$

Pierre-Yves Bienvenu, François Hennecart, Ilya Shkredov

Let $p$ a large enough prime number. When $A$ is a subset of $F_{p} ∖ {0}$ of cardinality $∣ A ∣ > (p + 1) /3$ , then an application of Cauchy-Davenport Theorem gives…

math.CO2018

A note on the Bilinear Bogolyubov Theorem: Transverse and bilinear sets

Pierre-Yves Bienvenu, Diego González-Sánchez, Ángel D. Martínez

A set $P \subset F_{p}^{n} \times F_{p}^{n}$ is called $bilinear$ when it is the zero set of a family of linear and bilinear forms, and $transverse$ when i…

math.NT2017★ 1 cited

Linear and quadratic uniformity of the Möbius function over $F_{q} [t]$

Pierre-Yves Bienvenu, Thái Hoàng Lê

We examine correlations of the Möbius function over $F_{q} [t]$ with linear or quadratic phases, that is, averages of the form \begin{equation} \label{eq:average} \frac{1}{q^…

math.CO2017

A bilinear Bogolyubov theorem

Pierre-Yves Bienvenu, Thái Hoàng Lê

The purpose of this note is to prove the existence of a remarkable structure in an iterated sumset derived from a set $P$ in a Cartesian square $F_{p}^{n} \times F_{p}^{n}$ …

math.CO2017

Polynomial equations in function fields

Pierre-Yves Bienvenu

The breakthrough paper of Croot, Lev, Pach \cite{CLP} on progression-free sets in $Z_{4}^{n}$ introduced a polynomial method that has generated a wealth of applications, such as Ellen…

math.NT2016

A higher-dimensional Siegel-Walfisz theorem

Pierre-Yves Bienvenu

The Green-Tao-Ziegler theorem provides asymptotics for the number of prime tuples of the form $(ψ_{1} (n), \dots, ψ_{t} (n))$ when $n$ ranges among the integer vectors of a convex body $K…

math.NT2015

Asymptotics for some polynomial patterns in the primes

Pierre-Yves Bienvenu

We prove asymptotic formulae for sums of the form $n \in Z^{d} \cap K \sum i = 1 \prod t F_{i} (ψ_{i} (n)),$ where $K$ is a convex body, each $F_{i}$ is either the von Mangoldt fun…

A Generalization of Sárközy's theorem in function fields

Additive index and Carlitz rank

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

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

Realisability of simultaneous density constraints for sets of integers

Intersective sets for sparse sets of integers

On algebraic properties of power monoids of numerical monoids

Metric decomposability theorems on sets of integers

A transference principle for systems of linear equations, and applications to almost twin primes

On additive bases in infinite abelian semigroups

Kneser's Theorem in σ-finite Abelian groups

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

A note on the set A(A+A)

A note on the Bilinear Bogolyubov Theorem: Transverse and bilinear sets

Linear and quadratic uniformity of the Möbius function over Fq​[t]

A bilinear Bogolyubov theorem

Polynomial equations in function fields

A higher-dimensional Siegel-Walfisz theorem

Asymptotics for some polynomial patterns in the primes

Kneser's Theorem in $σ$ -finite Abelian groups

A note on the set $A (A + A)$

Linear and quadratic uniformity of the Möbius function over $F_{q} [t]$