{"id":"https://openalex.org/W2900027927","doi":"https://doi.org/10.1080/00029890.2018.1507206","title":"Another Proof of the Famous Formula for the Zeta Function at Positive Even Integers","display_name":"Another Proof of the Famous Formula for the Zeta Function at Positive Even Integers","publication_year":2018,"publication_date":"2018-10-21","ids":{"openalex":"https://openalex.org/W2900027927","doi":"https://doi.org/10.1080/00029890.2018.1507206","mag":"2900027927"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1507206","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1507206","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/A5114374332","display_name":"Pedro Ribeiro","orcid":"https://orcid.org/0000-0002-5768-1383"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Pedro Ribeiro","raw_affiliation_strings":["Faculdade de C\u00eeencias da Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal"],"affiliations":[{"raw_affiliation_string":"Faculdade de C\u00eeencias da Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114374332"],"corresponding_institution_ids":["https://openalex.org/I182534213"],"apc_list":null,"apc_paid":null,"fwci":1.4474,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.81616028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"125","issue":"9","first_page":"839","last_page":"841"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9914000034332275,"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":0.9914000034332275,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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":0.9718999862670898,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7014259099960327},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.6465968489646912},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6291417479515076},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.6009682416915894},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.5261960625648499},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4924410283565521},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4791690409183502},{"id":"https://openalex.org/keywords/infinite-product","display_name":"Infinite product","score":0.46611979603767395},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.46327802538871765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3464752435684204},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1873892843723297}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7014259099960327},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.6465968489646912},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6291417479515076},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.6009682416915894},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.5261960625648499},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4924410283565521},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4791690409183502},{"id":"https://openalex.org/C138888516","wikidata":"https://www.wikidata.org/wiki/Q2266843","display_name":"Infinite product","level":2,"score":0.46611979603767395},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.46327802538871765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3464752435684204},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1873892843723297},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2018.1507206","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1507206","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W139421951","https://openalex.org/W1499599560","https://openalex.org/W1986164806","https://openalex.org/W1987049764","https://openalex.org/W1996715695","https://openalex.org/W2334305095","https://openalex.org/W2907457340"],"related_works":["https://openalex.org/W4388837814","https://openalex.org/W2095351586","https://openalex.org/W2041926118","https://openalex.org/W4318474536","https://openalex.org/W2003685798","https://openalex.org/W95230609","https://openalex.org/W2991019869","https://openalex.org/W2020775206","https://openalex.org/W1670038020","https://openalex.org/W2133090660"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3],"present":[4],"an":[5],"elementary":[6],"proof":[7,22],"of":[8,38,48],"the":[9,13,17,31,44,49],"classical":[10],"formula":[11],"for":[12],"zeta":[14],"function":[15],"at":[16],"positive":[18],"even":[19],"integers.":[20],"This":[21],"could":[23],"also":[24],"have":[25],"been":[26],"given":[27],"by":[28],"Euler":[29],"in":[30],"18th":[32],"century":[33],"since":[34],"it":[35],"uses":[36],"many":[37],"his":[39],"(sneaky)":[40],"analytic":[41],"techniques,":[42],"namely":[43],"infinite":[45],"product":[46],"representation":[47],"sine":[50],"function.":[51]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2019,"cited_by_count":3}],"updated_date":"2026-02-01T03:34:12.195049","created_date":"2025-10-10T00:00:00"}