{"id":"https://openalex.org/W7203610824","doi":"https://doi.org/10.48550/arxiv.2608.14241","title":"Ratio of sum of digits functions in two bases","display_name":"Ratio of sum of digits functions in two bases","publication_year":2026,"publication_date":"2026-08-14","ids":{"openalex":"https://openalex.org/W7203610824","doi":"https://doi.org/10.48550/arxiv.2608.14241"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.14241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14241","pdf_url":"https://arxiv.org/pdf/2608.14241","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2608.14241","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092720779","display_name":"Pascal Jelinek","orcid":"https://orcid.org/0009-0004-5877-2908","observed_orcids":["https://orcid.org/0009-0004-5877-2908"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jelinek, Pascal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5092720779"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.0003000000142492354,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/sum-of-digits-function","display_name":"sum of digits function","score":0.9919999837875366},{"id":"https://openalex.org/keywords/diophantine-approximation","display_name":"Diophantine approximation","score":0.5789999961853027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.836899995803833},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5965999960899353},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.522599995136261},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4952999949455261},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4927999973297119},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C2778975207","wikidata":"https://www.wikidata.org/wiki/Q7078836","display_name":"Of the form","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C105285975","wikidata":"https://www.wikidata.org/wiki/Q2719417","display_name":"Canonical normal form","level":2,"score":0.2606000006198883}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.14241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14241","pdf_url":"https://arxiv.org/pdf/2608.14241","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.14241","doi":"https://doi.org/10.48550/arxiv.2608.14241","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.14241","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.14241","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14241","pdf_url":"https://arxiv.org/pdf/2608.14241","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G190847146","display_name":"Correlations of k-regular and morphic sequences","funder_award_id":"P36137","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203610824.pdf","grobid_xml":"https://content.openalex.org/works/W7203610824.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2060101324","https://openalex.org/W4324092381","https://openalex.org/W4386043939","https://openalex.org/W4406032695","https://openalex.org/W4410220251","https://openalex.org/W4413087626","https://openalex.org/W4415961048","https://openalex.org/W4417409493"],"related_works":["https://openalex.org/W2982532122","https://openalex.org/W2101885939","https://openalex.org/W4297059861","https://openalex.org/W7223415031","https://openalex.org/W4294555808","https://openalex.org/W2007777736","https://openalex.org/W3099975487","https://openalex.org/W3150102919","https://openalex.org/W4407123423","https://openalex.org/W2093260197"],"abstract_inverted_index":{"In":[0,75],"2019":[1],"La":[2],"Bret\u00e8che,":[3],"Stoll":[4],"and":[5,24,62,90],"Tennenbaum":[6],"showed":[7],"that":[8,33,52,66,92],"the":[9,12,35,53,93,108,118],"ratio":[10,69,94],"of":[11,14,18,60,85,120],"sum":[13],"digits":[15],"function":[16],"$s_{q_1}(n)/s_{q_2}(n)$":[17],"two":[19],"multiplicatively":[20,86,109],"independent":[21,87],"bases":[22,88],"$q_1$":[23],"$q_2$":[25],"is":[26,70],"dense":[27],"in":[28,34,64,107,117],"$\\mathbb{Q}^+$.":[29],"Recently":[30],"Spiegelhofer":[31,44],"proved":[32],"special":[36],"case":[37,119],"$s_2(n)/s_3(n)=1$":[38],"we":[39,78],"have":[40],"infinitely":[41,72,99],"many":[42,73,100],"solutions.":[43],"extended":[45],"this":[46,76,105],"jointly":[47],"with":[48],"Drmota":[49],"to":[50],"show":[51,79],"pair":[54,84],"$(s_2(n),s_3(n))$":[55],"attains":[56,95],"almost":[57],"every":[58,67,96],"value":[59],"$\\mathbb{N}^2$":[61],"hence,":[63],"particular,":[65],"rational":[68,97],"attained":[71],"times.\\\\":[74],"paper":[77],"that,":[80],"indeed,":[81],"for":[82],"any":[83],"$p$":[89],"$q$,":[91],"number":[98],"times.":[101],"We":[102],"also":[103],"study":[104],"problem":[106],"dependent":[110],"case,":[111],"hence":[112],"giving":[113],"a":[114],"complete":[115],"characterisation":[116],"2":[121],"bases.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-18T00:00:00"}
