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arXiv · 2502.08624

Large sum-free subsets of sets of integers via $L^1$-estimates for trigonometric series

Benjamin Bedert
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Abstract

A set $B$ is said to be \emph{sum-free} if there are no $x,y,z\in B$ with $x+y=z$. We show that there exists a constant $c>0$ such that any set $A$ of $n$ integers contains a sum-free subset $A'$ of size $|A'|\geqslant n/3+c\log \log n$. This answers a longstanding problem in additive combinatorics, originally due to Erd\H{o}s.

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Benjamin Bedert. 2025-02-12. Large sum-free subsets of sets of integers via $L^1$-estimates for trigonometric series. https://arxiv.org/abs/2502.08624

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