Infinite Sumsets in Sets with Positive Density
Dynamical Systems
2024-02-23 v2 Combinatorics
Number Theory
Abstract
Motivated by questions asked by Erdos, we prove that any set with positive upper density contains, for any , a sumset , where are infinite. Our proof uses ergodic theory and relies on structural results for measure preserving systems. Our techniques are new, even for the previously known case of .
Cite
@article{arxiv.2206.01786,
title = {Infinite Sumsets in Sets with Positive Density},
author = {Bryna Kra and Joel Moreira and Florian K. Richter and Donald Robertson},
journal= {arXiv preprint arXiv:2206.01786},
year = {2024}
}
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49 Pages