Additive complements for a given asymptotic density

Alain Faisant (1) , Georges Grekos (1) , Ram Krishna Pandey , Teja Sai Somu

1 CTN - Combinatoire, théorie des nombres

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 last situation, we generalize our result to kA := {x 1 + · · · + x k : x i ∈ A, i = 1,. .. , k}. Article soumis pour publication, version 2. Version 1: https://arxiv.org/pdf/1809.07584.pdf

Domaines: Théorie des nombres [math.NT]

Alain Faisant, Georges Grekos, Ram Krishna Pandey, Teja Sai Somu. Additive complements for a given asymptotic density. Mediterranean Journal of Mathematics, 2021, 18, pp.25. ⟨10.1007/s00009-020-01679-0⟩. ⟨hal-02084758⟩