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

被引：7

作者：

Bienvenu, Pierre-Yves ^{[1
]}

Hennecart, Francois ^{[2
]}

机构：

[1] Univ Lyon, CNRS, ICJ UMR 5208, F-69622 Villeurbanne, France

[2] Univ Lyon, UJM St Etienne, CNRS, ICJ UMR 5208, F-42023 St Etienne, France

来源：

JOURNAL OF NUMBER THEORY | 2020年 / 212卷

关键词：

Sumsets; Asymptotic density; Haar measure; Sequences;

D O I：

10.1016/j.jnt.2019.11.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let d(A) be the asymptotic density (if it exists) of a sequence of integers A. For any real numbers 0 <= alpha <= beta <= 1, we solve the question of the existence of a sequence A of positive integers such that d(A) =alpha and d(A + A) = beta. More generally we study the set of k-tuples (d(iA))(1 <= i <= k) for A subset of N. This leads us to introduce subsets defined by diophantine constraints inside a random set of integers known as the set of "pseudo sth powers". We consider similar problems for subsets of the circle R/Z, that is, we partially determine the set of k-tuples (mu(iA))(1 <= i <= k )for A subset of R/Z. ( )(C) 2019 Elsevier Inc. All rights reserved.

引用

页码：285 / 310

页数：26