{"id":"https://openalex.org/W4411154405","doi":"https://doi.org/10.3390/axioms14060451","title":"A Class of the Generalized Ramanujan Tau Numbers and Their Associated Partition Functions","display_name":"A Class of the Generalized Ramanujan Tau Numbers and Their Associated Partition Functions","publication_year":2025,"publication_date":"2025-06-07","ids":{"openalex":"https://openalex.org/W4411154405","doi":"https://doi.org/10.3390/axioms14060451"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14060451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060451","pdf_url":"https://www.mdpi.com/2075-1680/14/6/451/pdf?version=1749430344","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/6/451/pdf?version=1749430344","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000018282","display_name":"Aleksandar Petojevi\u0107","orcid":"https://orcid.org/0000-0003-1491-165X"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Aleksandar Petojevi\u0107","raw_affiliation_strings":["Faculty of Education, University of Novi Sad, Podgori\u010dka 4, 25000 Sombor, Serbia"],"raw_orcid":"https://orcid.org/0000-0003-1491-165X","affiliations":[{"raw_affiliation_string":"Faculty of Education, University of Novi Sad, Podgori\u010dka 4, 25000 Sombor, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079512627","display_name":"H. M. Srivastava","orcid":"https://orcid.org/0000-0002-9277-8092"},"institutions":[{"id":"https://openalex.org/I151221077","display_name":"Chung Yuan Christian University","ror":"https://ror.org/02w8ws377","country_code":"TW","type":"education","lineage":["https://openalex.org/I151221077"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]},{"id":"https://openalex.org/I35928602","display_name":"Kyung Hee University","ror":"https://ror.org/01zqcg218","country_code":"KR","type":"education","lineage":["https://openalex.org/I35928602"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]},{"id":"https://openalex.org/I87490745","display_name":"Azerbaijan University","ror":"https://ror.org/00g1psz15","country_code":"AZ","type":"education","lineage":["https://openalex.org/I87490745"]}],"countries":["AZ","CA","IT","KR","TW"],"is_corresponding":true,"raw_author_name":"Hari M. Srivastava","raw_affiliation_strings":["Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea","Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan","Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ 1007 Baku, Azerbaijan","Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9277-8092","affiliations":[{"raw_affiliation_string":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea","institution_ids":["https://openalex.org/I35928602"]},{"raw_affiliation_string":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan","institution_ids":["https://openalex.org/I151221077"]},{"raw_affiliation_string":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ 1007 Baku, Azerbaijan","institution_ids":["https://openalex.org/I87490745"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050499945","display_name":"Sonja Orli\u0107","orcid":"https://orcid.org/0009-0007-6885-4394"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Sonja Orli\u0107","raw_affiliation_strings":["Faculty of Education, University of Novi Sad, Podgori\u010dka 4, 25000 Sombor, Serbia"],"raw_orcid":"https://orcid.org/0009-0007-6885-4394","affiliations":[{"raw_affiliation_string":"Faculty of Education, University of Novi Sad, Podgori\u010dka 4, 25000 Sombor, Serbia","institution_ids":["https://openalex.org/I170726198"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5079512627"],"corresponding_institution_ids":["https://openalex.org/I151221077","https://openalex.org/I184693016","https://openalex.org/I212119943","https://openalex.org/I35928602","https://openalex.org/I4210126829","https://openalex.org/I4210155399","https://openalex.org/I87490745"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18189273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"6","first_page":"451","last_page":"451"},"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":0.9995999932289124,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9980000257492065,"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/ramanujans-sum","display_name":"Ramanujan's sum","score":0.8821210861206055},{"id":"https://openalex.org/keywords/ramanujan-tau-function","display_name":"Ramanujan tau function","score":0.6669824719429016},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.647871732711792},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.647574245929718},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5815495848655701},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4909835159778595},{"id":"https://openalex.org/keywords/ramanujan-theta-function","display_name":"Ramanujan theta function","score":0.4701188802719116},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1414487659931183},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06488847732543945}],"concepts":[{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.8821210861206055},{"id":"https://openalex.org/C127808406","wikidata":"https://www.wikidata.org/wiki/Q3535240","display_name":"Ramanujan tau function","level":3,"score":0.6669824719429016},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.647871732711792},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.647574245929718},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5815495848655701},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4909835159778595},{"id":"https://openalex.org/C94047428","wikidata":"https://www.wikidata.org/wiki/Q2630765","display_name":"Ramanujan theta function","level":3,"score":0.4701188802719116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1414487659931183},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06488847732543945}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14060451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060451","pdf_url":"https://www.mdpi.com/2075-1680/14/6/451/pdf?version=1749430344","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fbcac90f3199406d9bd7f031e9b13612","is_oa":true,"landing_page_url":"https://doaj.org/article/fbcac90f3199406d9bd7f031e9b13612","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 6, p 451 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14060451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060451","pdf_url":"https://www.mdpi.com/2075-1680/14/6/451/pdf?version=1749430344","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411154405.pdf","grobid_xml":"https://content.openalex.org/works/W4411154405.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W654659464","https://openalex.org/W2007719507","https://openalex.org/W2016883155","https://openalex.org/W2065021342","https://openalex.org/W2066064595","https://openalex.org/W2986270851","https://openalex.org/W3027196102","https://openalex.org/W3028060585","https://openalex.org/W3190699790","https://openalex.org/W3205550270","https://openalex.org/W4363678269","https://openalex.org/W4386119892","https://openalex.org/W4386988875","https://openalex.org/W4395075247","https://openalex.org/W4399256286","https://openalex.org/W4407305136","https://openalex.org/W4407830179","https://openalex.org/W4409729619","https://openalex.org/W4410602670","https://openalex.org/W6872968894"],"related_works":["https://openalex.org/W1766818275","https://openalex.org/W2911192957","https://openalex.org/W4205985703","https://openalex.org/W2050882692","https://openalex.org/W2157136072","https://openalex.org/W4200519917","https://openalex.org/W2053691435","https://openalex.org/W4221011548","https://openalex.org/W2123424468","https://openalex.org/W4294610457"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,14,24,32,40,44,55],"authors":[4,30],"derive":[5,37],"some":[6],"believed-to-be":[7],"new":[8],"recursion":[9],"and":[10,36,50],"explicit":[11],"formulas":[12],"for":[13],"generalized":[15],"Ramanujan":[16],"numbers":[17,45],"\u03c4s(n)(s\u2208N\u222a{\u22121}),":[18],"where,":[19],"as":[20],"usual,":[21],"N":[22],"is":[23,70],"set":[25],"of":[26,39,52,54,74],"positive":[27],"integers.":[28],"The":[29,61],"consider":[31],"associated":[33],"partition":[34],"functions":[35],"connections":[38],"Eisenstein":[41],"series":[42],"with":[43],"\u03c4s(n).":[46],"Several":[47],"related":[48,71],"corollaries":[49],"consequences":[51],"each":[53],"presented":[56],"results":[57],"are":[58],"also":[59],"given.":[60],"paper":[62],"concludes":[63],"by":[64],"presenting":[65],"an":[66],"open":[67],"problem":[68],"that":[69],"to":[72],"one":[73],"these":[75],"results.":[76]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
