{"id":"https://openalex.org/W7203933588","doi":"https://doi.org/10.48550/arxiv.2608.20191","title":"Spectrum of the refined Diophantine exponent","display_name":"Spectrum of the refined Diophantine exponent","publication_year":2026,"publication_date":"2026-08-20","ids":{"openalex":"https://openalex.org/W7203933588","doi":"https://doi.org/10.48550/arxiv.2608.20191"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.20191","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20191","pdf_url":"https://arxiv.org/pdf/2608.20191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.20191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108869757","display_name":"Quang-Khai Nguyen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nguyen, Quang-Khai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5108869757"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6503999829292297,"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":0.6503999829292297,"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/T11567","display_name":"semigroups and automata theory","score":0.18619999289512634,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.04619999974966049,"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/infinite-words","display_name":"infinite words","score":0.9179999828338623},{"id":"https://openalex.org/keywords/ternary-alphabet","display_name":"ternary alphabet","score":0.9079999923706055},{"id":"https://openalex.org/keywords/liouville-numbers","display_name":"Liouville numbers","score":0.9929999709129333},{"id":"https://openalex.org/keywords/thue-morse-word","display_name":"Thue-Morse word","score":0.9980000257492065}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.8342000246047974},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.8177000284194946},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7141000032424927},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.6189000010490417},{"id":"https://openalex.org/C102966492","wikidata":"https://www.wikidata.org/wiki/Q1227061","display_name":"Diophantine approximation","level":3,"score":0.3889999985694885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3718999922275543},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.358599990606308},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2687999904155731},{"id":"https://openalex.org/C47600822","wikidata":"https://www.wikidata.org/wiki/Q7825032","display_name":"Topological dynamics","level":5,"score":0.2639000117778778}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.20191","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20191","pdf_url":"https://arxiv.org/pdf/2608.20191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2608.20191","doi":"https://doi.org/10.48550/arxiv.2608.20191","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.20191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.20191","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20191","pdf_url":"https://arxiv.org/pdf/2608.20191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G553375094","display_name":null,"funder_award_id":"101126554","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322676","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203933588.pdf","grobid_xml":"https://content.openalex.org/works/W7203933588.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4386269496","https://openalex.org/W7163073508","https://openalex.org/W7167904737"],"related_works":["https://openalex.org/W7221002058","https://openalex.org/W3127959870","https://openalex.org/W7214323766","https://openalex.org/W7214099643","https://openalex.org/W7171055890","https://openalex.org/W7214974008","https://openalex.org/W2039026476","https://openalex.org/W1995615896","https://openalex.org/W3021669009","https://openalex.org/W7214712869"],"abstract_inverted_index":{"The":[0],"refined":[1,44],"Diophantine":[2,45],"exponent,":[3],"recently":[4],"introduced":[5],"by":[6,85],"the":[7,14,40,43,62,73],"author,":[8],"is":[9,47],"a":[10,37,83],"quantity":[11],"that":[12,52],"measures":[13],"periodicity":[15],"of":[16,42,61,64],"an":[17],"infinite":[18],"word.":[19],"In":[20],"this":[21,25,53],"article,":[22],"we":[23,33,50,68],"study":[24],"exponent":[26,46,54],"from":[27,81],"combinatorial":[28],"and":[29,76,87],"topological":[30,56],"viewpoints.":[31],"First,":[32],"show":[34,51],"that,":[35],"over":[36],"ternary":[38],"alphabet,":[39],"spectrum":[41],"$[1,\\infty]$.":[48],"Second,":[49],"has":[55],"properties":[57],"similar":[58],"to":[59],"those":[60],"set":[63],"Liouville":[65],"numbers.":[66],"Finally,":[67],"provide":[69],"concrete":[70],"examples":[71],"with":[72],"Champernowne,":[74],"Rudin--Shapiro,":[75],"Thue--Morse":[77],"words,":[78],"words":[79],"coming":[80],"coding":[82],"rotation":[84],"intervals,":[86],"bracket":[88],"words.":[89]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-22T00:00:00"}
