On the density or measure of sets and their sumsets in the integers or the circle - Combinatoire, théorie des nombres Accéder directement au contenu
Article Dans Une Revue Journal of Number Theory Année : 2020

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

Résumé

Let $\mathrm{d}(A)$ be the asymptotic density (if it exists) of a sequence of integers $A$. For any real numbers $0\leq\alpha\leq\beta\leq 1$, we solve the question of the existence of a sequence $A$ of positive integers such that $\mathrm{d}(A)=\alpha$ and $\mathrm{d}(A+A)=\beta$. More generally we study the set of $k$-tuples $(\mathrm{d}(iA))_{1\leq i\leq k}$ for $A\subset \mathbb{N}$. This leads us to introduce subsets defined by diophantine constraints inside a random set of integers known as the set of ``pseudo $s$th powers''. We consider similar problems for subsets of the circle $\mathbb{R}/\mathbb{Z}$, that is, we partially determine the set of $k$-tuples $(\mu(iA))_{1\leq i\leq k}$ for $A\subset \mathbb{R}/\mathbb{Z}$.
Fichier principal
Vignette du fichier
S0022314X19304044.pdf (458.45 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02140489 , version 1 (20-05-2022)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

Citer

Pierre-Yves Bienvenu, François Hennecart. On the density or measure of sets and their sumsets in the integers or the circle. Journal of Number Theory, inPress, ⟨10.1016/j.jnt.2019.11.004⟩. ⟨hal-02140489⟩
43 Consultations
88 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More