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On Hölder maps and prime gaps
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dc.contributor.author | Chen, Haipeng | |
dc.contributor.author | Fraser, Jonathan | |
dc.date.accessioned | 2022-11-08T00:43:17Z | |
dc.date.available | 2022-11-08T00:43:17Z | |
dc.date.issued | 2021-11-08 | |
dc.identifier | 273831635 | |
dc.identifier | 9de5a449-3602-42f1-a7a4-c66c13899e5c | |
dc.identifier | 000731614700020 | |
dc.identifier | 85125118675 | |
dc.identifier.citation | Chen , H & Fraser , J 2021 , ' On Hölder maps and prime gaps ' , Real Analysis Exchange , vol. 46 , no. 2 , pp. 523-532 . https://doi.org/10.14321/realanalexch.46.2.0523 | en |
dc.identifier.issn | 0147-1937 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/106838099 | |
dc.identifier.uri | https://hdl.handle.net/10023/26321 | |
dc.description | Funding: 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.abstract | Let 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.format.extent | 285295 | |
dc.language.iso | eng | |
dc.relation.ispartof | Real Analysis Exchange | en |
dc.subject | Prime | en |
dc.subject | Prime gaps | en |
dc.subject | Cramér’s conjecture | en |
dc.subject | Hölder maps | en |
dc.subject | Lipschitz maps | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On Hölder maps and prime gaps | 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.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.14321/realanalexch.46.2.0523 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2022-11-08 | |
dc.identifier.grantnumber | EP/R015104/1 | en |
dc.identifier.grantnumber | RPG-2019-034 | en |
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