Approximate arithmetic structure in large sets of integers

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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(Δα) for any α∈(0,1).
Original languageEnglish
Pages (from-to)163-174
JournalReal Analysis Exchange
Volume46
Issue number1
Early online date14 Oct 2021
DOIs
Publication statusPublished - 2021

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