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Effective bounds for Roth's theorem with shifted square common difference
Published 15 Sep 2023 in math.NT and math.CO | (2309.08359v1)
Abstract: Let $S$ be a subset of ${1,\ldots,N}$ avoiding the nontrivial progressions $x, x+y2-1, x+ 2(y2-1)$. We prove that $|S|\ll N/\log_m{N}$, where $\log_m $ is the $m$-fold iterated logarithm and $m\in\mathbf{N}$ is an absolute constant. This answers a question of Green.
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