Files in this item
Approximate arithmetic structure in large sets of integers
Item metadata
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 | 269404999 | |
dc.identifier | 5d2dcc8a-3fdc-439f-a0aa-756cc5876ddc | |
dc.identifier | 000731613000009 | |
dc.identifier | 85120806327 | |
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 | ORCID: /0000-0002-8066-9120/work/102330469 | |
dc.identifier.uri | https://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.format.extent | 2648508 | |
dc.language.iso | eng | |
dc.relation.ispartof | Real Analysis Exchange | 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.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 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 |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.