{"id":"https://openalex.org/W7222997440","doi":"https://doi.org/10.48550/arxiv.2610.26622","title":"On the denominators of signed harmonic sums","display_name":"On the denominators of signed harmonic sums","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7222997440","doi":"https://doi.org/10.48550/arxiv.2610.26622"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.26622","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26622","pdf_url":"https://arxiv.org/pdf/2610.26622","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/2610.26622","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014829039","display_name":"Yang Quan-Hui","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yang, Quan-Hui","raw_affiliation_strings":["Ministry of Education Key Laboratory for NSLSCS , Nanjing Normal University , Nanjing 210023 , P.R. China","School of Mathematical Sciences and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education Key Laboratory for NSLSCS , Nanjing Normal University , Nanjing 210023 , P.R. China","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"School of Mathematical Sciences and","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014829039"],"corresponding_institution_ids":["https://openalex.org/I152031979"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.9980000257492065,"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":0.9980000257492065,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.00139999995008111,"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":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/denominators","display_name":"denominators","score":0.6299999952316284},{"id":"https://openalex.org/keywords/harmonic-series","display_name":"harmonic series","score":0.621999979019165},{"id":"https://openalex.org/keywords/asymptotic-density","display_name":"asymptotic density","score":0.8930000066757202},{"id":"https://openalex.org/keywords/rational-approximation","display_name":"rational approximation","score":0.4359999895095825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.803600013256073},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7206000089645386},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.5360999703407288},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.5353999733924866},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5274999737739563},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5008999705314636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4244000017642975},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.3330000042915344},{"id":"https://openalex.org/C156491182","wikidata":"https://www.wikidata.org/wiki/Q752723","display_name":"Natural density","level":2,"score":0.311599999666214},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.2734000086784363}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.26622","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26622","pdf_url":"https://arxiv.org/pdf/2610.26622","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.2610.26622","doi":"https://doi.org/10.48550/arxiv.2610.26622","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.26622","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:2610.26622","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26622","pdf_url":"https://arxiv.org/pdf/2610.26622","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/G1405383360","display_name":null,"funder_award_id":"12371005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222997440.pdf","grobid_xml":"https://content.openalex.org/works/W7222997440.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2081319812","https://openalex.org/W2082356156","https://openalex.org/W2318575377","https://openalex.org/W2569886217","https://openalex.org/W2766280836","https://openalex.org/W2807990773","https://openalex.org/W2963506483","https://openalex.org/W3107238644","https://openalex.org/W3196223354","https://openalex.org/W4295178915"],"related_works":["https://openalex.org/W2963506483","https://openalex.org/W4380089228","https://openalex.org/W3107238644","https://openalex.org/W2766280836","https://openalex.org/W4391535407","https://openalex.org/W4210684463","https://openalex.org/W4295178915","https://openalex.org/W7206209601","https://openalex.org/W4404395984","https://openalex.org/W2468811695"],"abstract_inverted_index":{"Let":[0],"$\\eps=(\\eps_i)_{i\\ge1}$":[1],"be":[2,10],"a":[3,50],"sequence":[4,45],"with":[5,37],"$\\eps_i\\in\\{-1,1\\}$,":[6],"and":[7,54],"let":[8],"$v_n(\\eps)$":[9],"the":[11,31],"positive":[12,34],"denominator":[13],"of":[14,33,46,52],"$\\sum_{i=1}^n\\eps_i/i$":[15],"in":[16,27],"lowest":[17],"terms.":[18],"We":[19],"prove":[20],"that":[21],"$|\\{1\\le":[22],"n\\le":[23],"x:v_n(\\eps)\\ne":[24],"v_{n+1}(\\eps)\\}|=o(x)$":[25],"uniformly":[26],"$\\eps$.":[28],"In":[29],"particular,":[30],"set":[32],"integers":[35],"$n$":[36],"$v_n(\\eps)=v_{n+1}(\\eps)$":[38],"has":[39],"asymptotic":[40],"density":[41],"one":[42],"for":[43],"every":[44],"signs.":[47],"This":[48],"answers":[49],"problem":[51],"Wu":[53],"Chen,":[55],"\\emph{J.":[56],"Number":[57],"Theory}":[58],"\\textbf{200}":[59],"(2019),":[60],"397--406.":[61]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}