Additive Complements for a given Asymptotic Density

2018/09/20 by Alain Faisant, Faisant, Alain, Georges Grekos +5
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1809.07584

13 pages

arxiv created 2019/12/21 · arxiv updated 2019/12/24

Abstract

The first version of this text was written and submitted to a journal on April, 12, 2018. This second version was submitted on April, 9, 2019. We investigate the existence of subsets A and B of ℕ:=\0,1,2,…\ such that the sumset A+B:=\a+b~;a∈ A,b∈ B\ has given asymptotic density. We solve the particular case in which B is a given finite subset of ℕ and also the case when B=A ; in the later case, we generalize our result to kA:=\x₁+⋯+x_k: x_i∈ A, i=1,…,k\ for an integer k≥2.

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