{"id":"https://openalex.org/W2792482408","doi":"https://doi.org/10.1080/00029890.2018.1420996","title":"Subsums of the Harmonic Series","display_name":"Subsums of the Harmonic Series","publication_year":2018,"publication_date":"2018-03-22","ids":{"openalex":"https://openalex.org/W2792482408","doi":"https://doi.org/10.1080/00029890.2018.1420996","mag":"2792482408"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1420996","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1420996","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024415309","display_name":"Brian Lubeck","orcid":null},"institutions":[{"id":"https://openalex.org/I26538001","display_name":"San Diego State University","ror":"https://ror.org/0264fdx42","country_code":"US","type":"education","lineage":["https://openalex.org/I26538001"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Brian Lubeck","raw_affiliation_strings":["San Diego State University, 5500 Campanile Dr., San Diego, CA 92182-7720"],"affiliations":[{"raw_affiliation_string":"San Diego State University, 5500 Campanile Dr., San Diego, CA 92182-7720","institution_ids":["https://openalex.org/I26538001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071624615","display_name":"Vadim Ponomarenko","orcid":"https://orcid.org/0000-0002-1174-3366"},"institutions":[{"id":"https://openalex.org/I26538001","display_name":"San Diego State University","ror":"https://ror.org/0264fdx42","country_code":"US","type":"education","lineage":["https://openalex.org/I26538001"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vadim Ponomarenko","raw_affiliation_strings":["San Diego State University, 5500 Campanile Dr., San Diego, CA 92182-7720"],"affiliations":[{"raw_affiliation_string":"San Diego State University, 5500 Campanile Dr., San Diego, CA 92182-7720","institution_ids":["https://openalex.org/I26538001"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024415309"],"corresponding_institution_ids":["https://openalex.org/I26538001"],"apc_list":null,"apc_paid":null,"fwci":1.4654,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.78528996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"125","issue":"4","first_page":"351","last_page":"355"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9488000273704529,"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":0.9488000273704529,"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/T10244","display_name":"Chaos control and synchronization","score":0.9419999718666077,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9259999990463257,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.7548971176147461},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3204604983329773},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.17557162046432495}],"concepts":[{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.7548971176147461},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3204604983329773},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.17557162046432495},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2018.1420996","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1420996","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W2061496873","https://openalex.org/W2312441253","https://openalex.org/W2312816643","https://openalex.org/W2320495939","https://openalex.org/W2324605242","https://openalex.org/W2328892375","https://openalex.org/W2403596028","https://openalex.org/W2963387285","https://openalex.org/W4232586510","https://openalex.org/W4234684993","https://openalex.org/W4246298670","https://openalex.org/W4247532318","https://openalex.org/W4248742736","https://openalex.org/W4253174192"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"We":[0,13],"consider":[1],"subsums":[2],"of":[3,23],"the":[4],"harmonic":[5],"series,":[6],"and":[7],"determine":[8,18],"conditions":[9,16],"for":[10,20],"their":[11],"convergence.":[12],"apply":[14],"these":[15],"to":[17],"convergence":[19],"a":[21],"family":[22],"series":[24],"that":[25],"generalizes":[26],"Kempner\u2019s":[27],"series.":[28]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
