Approximate arithmetic structure in large sets of integers

Fraser, Jonathan; Yu, Han

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dc.contributor.author	Fraser, Jonathan
dc.contributor.author	Yu, Han
dc.date.accessioned	2022-10-13T23:40:22Z
dc.date.available	2022-10-13T23:40:22Z
dc.date.issued	2021
dc.identifier.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	en
dc.identifier.issn	0147-1937
dc.identifier.other	PURE: 269404999
dc.identifier.other	PURE UUID: 5d2dcc8a-3fdc-439f-a0aa-756cc5876ddc
dc.identifier.other	ORCID: /0000-0002-8066-9120/work/102330469
dc.identifier.other	WOS: 000731613000009
dc.identifier.other	Scopus: 85120806327
dc.identifier.uri	http://hdl.handle.net/10023/26191
dc.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).	en
dc.description.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).
dc.language.iso	eng
dc.relation.ispartof	Real Analysis Exchange	en
dc.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.	en
dc.subject	QA Mathematics	en
dc.subject	T-NDAS	en
dc.subject.lcc	QA	en
dc.title	Approximate arithmetic structure in large sets of integers	en
dc.type	Journal article	en
dc.contributor.sponsor	EPSRC	en
dc.contributor.sponsor	The Leverhulme Trust	en
dc.description.version	Postprint	en
dc.contributor.institution	University of St Andrews. Pure Mathematics	en
dc.identifier.doi	https://doi.org/10.14321/realanalexch.46.1.0163
dc.description.status	Peer reviewed	en
dc.date.embargoedUntil	2022-10-14
dc.identifier.url	https://www.jstor.org/journal/realanalexch	en
dc.identifier.url	https://projecteuclid.org/journals/real-analysis-exchange/issues	en
dc.identifier.url	https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Approximate-arithmetic-structure-in-large-sets-of-integers/10.14321/realanalexch.46.1.0163.short	en
dc.identifier.grantnumber	EP/R015104/1	en
dc.identifier.grantnumber	RPG-2019-034	en

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