{"id":"https://openalex.org/W2594953169","doi":"https://doi.org/10.1080/10586458.2017.1301841","title":"A Lower Bound for the Dimension of Bernoulli Convolutions","display_name":"A Lower Bound for the Dimension of Bernoulli Convolutions","publication_year":2017,"publication_date":"2017-04-05","ids":{"openalex":"https://openalex.org/W2594953169","doi":"https://doi.org/10.1080/10586458.2017.1301841","mag":"2594953169"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2017.1301841","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1301841","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.manchester.ac.uk/en/publications/ec56b714-2fe0-4e1a-b095-5fa7e86df1c2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077238894","display_name":"Kevin G. Hare","orcid":"https://orcid.org/0000-0003-4864-4721"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Kevin G. Hare","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081904890","display_name":"Nikita Sidorov","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Nikita Sidorov","raw_affiliation_strings":["School of Mathematics, The University of Manchester, Manchester, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, The University of Manchester, Manchester, United Kingdom","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077238894"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":1.4922,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.7933757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"27","issue":"4","first_page":"414","last_page":"418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9757000207901001,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/beta","display_name":"BETA (programming language)","score":0.7576042413711548},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.7093406915664673},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6868637800216675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6273626089096069},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5948629379272461},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5489030480384827},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4233863353729248},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4142734408378601},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3862752318382263},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17219498753547668},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08271262049674988},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.05069279670715332}],"concepts":[{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.7576042413711548},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.7093406915664673},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6868637800216675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6273626089096069},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5948629379272461},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5489030480384827},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4233863353729248},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4142734408378601},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3862752318382263},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17219498753547668},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08271262049674988},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.05069279670715332},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2017.1301841","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1301841","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire/ec56b714-2fe0-4e1a-b095-5fa7e86df1c2","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/ec56b714-2fe0-4e1a-b095-5fa7e86df1c2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hare, K G & Sidorov, N 2017, 'A Lower Bound for the Dimension of Bernoulli Convolutions', Experimental Mathematics, pp. 1-5. https://doi.org/10.1080/10586458.2017.1301841","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1609.02131","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.02131","pdf_url":"https://arxiv.org/pdf/1609.02131","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/ec56b714-2fe0-4e1a-b095-5fa7e86df1c2","is_oa":true,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/a-lower-bound-for-the-dimension-of-bernoulli-convolutions(ec56b714-2fe0-4e1a-b095-5fa7e86df1c2).html","pdf_url":"https://pure.manchester.ac.uk/ws/files/55114982/hs2016v2.pdf","source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Hare, K G & Sidorov, N 2017, 'A Lower Bound for the Dimension of Bernoulli Convolutions', Experimental Mathematics, pp. 1-5. https://doi.org/10.1080/10586458.2017.1301841","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/ec56b714-2fe0-4e1a-b095-5fa7e86df1c2","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/ec56b714-2fe0-4e1a-b095-5fa7e86df1c2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hare, K G & Sidorov, N 2017, 'A Lower Bound for the Dimension of Bernoulli Convolutions', Experimental Mathematics, pp. 1-5. https://doi.org/10.1080/10586458.2017.1301841","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1597412403","display_name":null,"funder_award_id":"RGPIN-","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G1749632606","display_name":null,"funder_award_id":"RGPIN-2014","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2144554729","display_name":null,"funder_award_id":"RGPIN-2014-0","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3216283581","display_name":null,"funder_award_id":"RGPIN-201","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5233204378","display_name":null,"funder_award_id":"RGPIN-2014-03154","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6221715925","display_name":null,"funder_award_id":"RGPIN","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G99476218","display_name":null,"funder_award_id":"RGPIN-2014-03","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1586178749","https://openalex.org/W1604601822","https://openalex.org/W2014573070","https://openalex.org/W2036561890","https://openalex.org/W2069372848","https://openalex.org/W2075595154","https://openalex.org/W2089164015","https://openalex.org/W2110292682","https://openalex.org/W2113119296","https://openalex.org/W2161155863","https://openalex.org/W2166790954","https://openalex.org/W2269341939","https://openalex.org/W2288625294","https://openalex.org/W2321521606","https://openalex.org/W2325571074","https://openalex.org/W2509647992","https://openalex.org/W2544904738","https://openalex.org/W2963166899","https://openalex.org/W3020808117","https://openalex.org/W3099200545","https://openalex.org/W3100187951","https://openalex.org/W4212896099","https://openalex.org/W4254501766"],"related_works":["https://openalex.org/W1619264321","https://openalex.org/W2899588557","https://openalex.org/W4254565718","https://openalex.org/W3094386089","https://openalex.org/W2180382450","https://openalex.org/W2129020938","https://openalex.org/W4298392611","https://openalex.org/W1980594489","https://openalex.org/W4253643872","https://openalex.org/W2094680711"],"abstract_inverted_index":{"Let":[0],"\u03b2":[1,31,55,67],"\u2208":[2,32,56],"(1,":[3,33,57],"2)":[4,34],"and":[5,35,48],"let":[6],"H\u03b2":[7,26],"denote":[8],"Garsia\u2019s":[9],"entropy":[10],"for":[11,29,39,53,72,81],"the":[12,20],"Bernoulli":[13],"convolution":[14],"\u03bc\u03b2":[15],"associated":[16],"with":[17,43],"\u03b2.":[18],"In":[19,59],"present":[21],"article":[22],"we":[23,61],"show":[24,62],"that":[25,63,70],">":[27],"0.82":[28],"all":[30,54],"improve":[36],"this":[37,50],"bound":[38],"certain":[40],"ranges.":[41],"Combined":[42],"recent":[44],"results":[45],"by":[46],"Hochman":[47],"Breuillard-Varj\u00fa,":[49],"yields":[51],"dim(\u03bc\u03b2)\u22650.82":[52],"2).":[58],"addition,":[60],"if":[64],"an":[65],"algebraic":[66],"is":[68,90],"such":[69],"[Q(\u03b2):Q(\u03b2k)]=k":[71],"some":[73],"k":[74],"\u2a7e":[75],"2,":[76],"then":[77],"dim(\u03bc\u03b2)=1.":[78],"Such":[79],"is,":[80],"instance,":[82],"any":[83],"root":[84],"of":[85],"a":[86,92],"Pisot":[87,93],"number":[88,94],"which":[89],"not":[91],"itself.":[95]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2020-11-23T00:00:00"}
