Approximate arithmetic structure in large sets of integers
Date
2021Grant ID
EP/R015104/1
RPG-2019-034
Metadata
Show full item recordAltmetrics Handle Statistics
Altmetrics DOI Statistics
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).
Citation
Fraser , J & Yu , H 2021 , ' Approximate arithmetic structure in large sets of integers ' , Real Analysis Exchange , vol. 46 , no. 1 , pp. 163-174 . https://doi.org/10.14321/realanalexch.46.1.0163
Publication
Real Analysis Exchange
Status
Peer reviewed
ISSN
0147-1937Type
Journal article
Rights
Copyright © 2021 Real Exchange Analysis. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.14321/realanalexch.46.1.0163.
Description
Funding: JMF acknowledges financial support from an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). HY was financially supported by the University of St Andrews and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No.803711).Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.