English

On the Sum of Dilations of a Set

Number Theory 2013-11-20 v2

Abstract

We show that for any relatively prime integers 1p<q1\leq p<q and for any finite AZA \subset \mathbb{Z} one has pA+qA(p+q)A(pq)(p+q3)(p+q)+1.|p \cdot A + q \cdot A | \geq (p + q) |A| - (pq)^{(p+q-3)(p+q) + 1}.

Keywords

Cite

@article{arxiv.1311.0422,
  title  = {On the Sum of Dilations of a Set},
  author = {Antal Balog and George Shakan},
  journal= {arXiv preprint arXiv:1311.0422},
  year   = {2013}
}