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dc.contributor.authorChen, Haipeng
dc.contributor.authorFraser, Jonathan
dc.identifier.citationChen , H & Fraser , J 2021 , ' On Hölder maps and prime gaps ' , Real Analysis Exchange , vol. 46 , no. 2 , pp. 523-532 .
dc.identifier.otherPURE: 273831635
dc.identifier.otherPURE UUID: 9de5a449-3602-42f1-a7a4-c66c13899e5c
dc.identifier.otherORCID: /0000-0002-8066-9120/work/106838099
dc.identifier.otherWOS: 000731614700020
dc.identifier.otherScopus: 85125118675
dc.descriptionFunding: The research of H. Chen was funded by China Scholarship Council (File No. 201906150102). J. M.Fraser was financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034).en
dc.description.abstractLet pn denote the nth prime, and consider the function 1/n → 1/pn which maps the reciprocals of the positive integers bijectively to the reciprocals of the primes. We show that Hölder continuity of this function is equivalent to a parametrised family of Cramér type estimates on the gaps between successive primes. Here the parametrisation comes from the Hölder exponent. In particular, we show that Cramér’s conjecture is equivalent to the map 1/n → 1/pn being Lipschitz. On the other hand, we show that the inverse map 1/pn → 1/n is Hölder of all orders but not Lipschitz and this is independent of Cramér’s conjecture.
dc.relation.ispartofReal Analysis Exchangeen
dc.rightsCopyright © 2021 Michigan State University Press. 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
dc.subjectPrime gapsen
dc.subjectCramér’s conjectureen
dc.subjectHölder mapsen
dc.subjectLipschitz mapsen
dc.subjectQA Mathematicsen
dc.titleOn Hölder maps and prime gapsen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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