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Infinite sumsets in sets with positive density
- Publication Year :
- 2023
- Publisher :
- American Mathematical Society (AMS), 2023.
-
Abstract
- Motivated by questions asked by Erdos, we prove that any set $A\subset{\mathbb N}$ with positive upper density contains, for any $k\in{\mathbb N}$, a sumset $B_1+\cdots+B_k$, where $B_1,\dots,B_k\subset{\mathbb N}$ 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 $k=2$.<br />Comment: 49 Pages
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....4ef3d2a42013dda0462042e5ac59720a