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arXiv · 1905.05034

Approximate arithmetic structure in large sets of integers

Jonathan M. Fraser·Han Yu
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Abstract

We prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arithmetic progressions in a strong quantitative sense. More specifically, expressing the error in the approximation in terms of the gap length $Δ$ of the progression, we improve a previous result of $o(Δ)$ to $O(Δ^α)$ for any $α\in (0,1)$.

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Jonathan M. Fraser, Han Yu. 2019-05-13. Approximate arithmetic structure in large sets of integers. https://arxiv.org/abs/1905.05034

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