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arXiv · 2603.27045

Improved Bounds for 3-Progressions

Rushil Raghavan
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Abstract

We prove that if $A\subset \{1,\dots,N\}$ has no nontrivial three-term arithmetic progressions, then $|A|\leq \exp(-c\log(N)^{1/6}\log\log(N)^{-1})N$ for some absolute constant $c>0$. To obtain this bound, we use an iterated variant of the sifting argument of Kelley and Meka, as well as an improved bootstrapping argument for Croot-Sisask almost-periodicity due to Bloom and Sisask.

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Rushil Raghavan. 2026-03-27. Improved Bounds for 3-Progressions. https://arxiv.org/abs/2603.27045

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