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Abstract:Let $A$ be a subset of $G$, where $G$ is a finite abelian group of torsion $r$. It was conjectured by Ruzsa that if $|A+A|\leq K|A|$, then $A$ is contained in a coset of $G$ of size at most $r^{CK}|A|$ for some constant $C$. The case $r=2$ received considerable attention in a sequence of papers, and was resolved by Green and Tao. Recently, Even-Zohar and Lovett settled the case when $r$ is a prime. In this paper, we confirm the conjecture when $r$ is a power of prime. In particular, the bound we obtain is tight.
From: Yifan Jing [view email]
[v1]
Thu, 17 Jan 2019 03:49:54 UTC (11 KB)
[v2]
Tue, 29 Jan 2019 21:17:30 UTC (11 KB)
[v3]
Mon, 14 Sep 2026 02:40:16 UTC (1 KB) (withdrawn)
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