{"id":"https://openalex.org/W2566080594","doi":"https://doi.org/10.1080/00029890.2020.1668716","title":"Generalization of a Ramanujan Identity","display_name":"Generalization of a Ramanujan Identity","publication_year":2019,"publication_date":"2019-12-19","ids":{"openalex":"https://openalex.org/W2566080594","doi":"https://doi.org/10.1080/00029890.2020.1668716","mag":"2566080594"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1668716","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1668716","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1612.08307","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002582447","display_name":"\u00d6rs Reb\u00e1k","orcid":"https://orcid.org/0000-0002-3342-0664"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"\u00d6rs Reb\u00e1k","raw_affiliation_strings":["Independent Scholar, Gy\u0151r, Hungary"],"affiliations":[{"raw_affiliation_string":"Independent Scholar, Gy\u0151r, Hungary","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002582447"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01097741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"127","issue":"1","first_page":"80","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9993000030517578,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.9686338305473328},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.6498138904571533},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5902706980705261},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5900298953056335},{"id":"https://openalex.org/keywords/ramanujan-theta-function","display_name":"Ramanujan theta function","score":0.4991264343261719},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4809838533401489},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22907310724258423},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1744072437286377}],"concepts":[{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.9686338305473328},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.6498138904571533},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5902706980705261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5900298953056335},{"id":"https://openalex.org/C94047428","wikidata":"https://www.wikidata.org/wiki/Q2630765","display_name":"Ramanujan theta function","level":3,"score":0.4991264343261719},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4809838533401489},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22907310724258423},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1744072437286377},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00029890.2020.1668716","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1668716","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"},{"id":"pmh:oai:arXiv.org:1612.08307","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.08307","pdf_url":"https://arxiv.org/pdf/1612.08307","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":"mag:2566080594","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1612.08307.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1612.08307","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1612.08307","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1612.08307","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.08307","pdf_url":"https://arxiv.org/pdf/1612.08307","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1555475515","https://openalex.org/W1569990823","https://openalex.org/W2059140607","https://openalex.org/W2071565129","https://openalex.org/W2595945369","https://openalex.org/W4232593792","https://openalex.org/W4241654653","https://openalex.org/W4299584580"],"related_works":["https://openalex.org/W3002492186","https://openalex.org/W2994916873","https://openalex.org/W2313485111","https://openalex.org/W2011868831","https://openalex.org/W2158486378","https://openalex.org/W1734041700","https://openalex.org/W619955411","https://openalex.org/W2953484358","https://openalex.org/W3141722702","https://openalex.org/W3150435967","https://openalex.org/W3088204784","https://openalex.org/W2893244011","https://openalex.org/W2763271675","https://openalex.org/W982788438","https://openalex.org/W120059926","https://openalex.org/W3203499738","https://openalex.org/W1208872669","https://openalex.org/W1835491228","https://openalex.org/W3120525152","https://openalex.org/W2089935872"],"abstract_inverted_index":{"The":[0],"Euler":[1],"product":[2],"for":[3],"the":[4,29,35],"Landau\u2013Ramanujan":[5],"constant":[6],"could":[7],"have":[8],"motivated":[9],"a":[10,25,66],"curious":[11],"identity":[12,44],"by":[13],"Ramanujan":[14],"that":[15],"appears":[16],"in":[17],"his":[18],"notebooks":[19],"two":[20],"times.":[21],"This":[22],"observation":[23],"involves":[24],"square":[26],"root":[27],"and":[28],"first":[30],"four":[31],"prime":[32],"numbers":[33],"of":[34,55],"form":[36],"4n+3,":[37],"i.e.,":[38],"3,7,11,19.":[39],"Berndt":[40],"asks":[41],"whether":[42],"Ramanujan\u2019s":[43],"is":[45],"an":[46],"isolated":[47],"result,":[48],"or":[49],"if":[50],"there":[51],"are":[52],"other":[53],"identities":[54],"this":[56,59],"type.":[57],"With":[58],"work":[60],"we":[61],"would":[62],"like":[63],"to":[64,69],"give":[65],"possible":[67],"answer":[68],"Berndt\u2019s":[70],"question.":[71]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
