Improved Bounds for 3-Progressions

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1. Verfasser: Raghavan, Rushil
Format: Preprint
Veröffentlicht: 2026
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author Raghavan, Rushil
author_facet Raghavan, Rushil
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_27045
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Improved Bounds for 3-Progressions
Raghavan, Rushil
Number Theory
Combinatorics
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.
title Improved Bounds for 3-Progressions
topic Number Theory
Combinatorics
url https://arxiv.org/abs/2603.27045