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Dimensions of the popcorn graph

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dc.contributor.authorChen, Haipeng
dc.contributor.authorFraser, Jonathan
dc.contributor.authorYu, Han
dc.date.accessioned2022-01-06T10:30:11Z
dc.date.available2022-01-06T10:30:11Z
dc.date.issued2022-08-18
dc.identifier277310834
dc.identifier23b4c7bf-62f9-4e1d-b289-3b152bb7f928
dc.identifier000843273100001
dc.identifier85139508323
dc.identifier.citationChen , H , Fraser , J & Yu , H 2022 , ' Dimensions of the popcorn graph ' , Proceedings of the American Mathematical Society , vol. 150 , pp. 4729-4742 . https://doi.org/10.1090/proc/15729en
dc.identifier.issn0002-9939
dc.identifier.otherORCID: /0000-0002-8066-9120/work/123196187
dc.identifier.urihttps://hdl.handle.net/10023/24605
dc.descriptionFunding: H. Chen is thankful for the excellent atmosphere for research provided by the University of St Andrews. H. Chen was funded by China Scholarship Council (File No. 201906150102) and NSFC (No. 11601161, 11771153 and 11871227). J. M. Fraser was supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). H. Yu was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 803711), and indirectly by Corpus Christi College, Cambridge.en
dc.description.abstractThe 'popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimension and Assouad spectrum. The main ingredients include Duffin-Schaeffer type estimates from Diophantine approximation and the Chung-Erdős inequality from probability theory.
dc.format.extent430345
dc.language.isoeng
dc.relation.ispartofProceedings of the American Mathematical Societyen
dc.subjectPopcorn functionen
dc.subjectThomae functionen
dc.subjectBox dimensionen
dc.subjectAssouad dimensionen
dc.subjectAssouad spectrumen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleDimensions of the popcorn graphen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
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.identifier.doi10.1090/proc/15729
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/2007.08407en
dc.identifier.grantnumberEP/R015104/1en
dc.identifier.grantnumberRPG-2019-034en


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