{"id":"https://openalex.org/W7220709447","doi":"https://doi.org/10.48550/arxiv.2610.04770","title":"Borwein-Bradley-type identities for Ramanujan-type series for $1/\u03c0^4$","display_name":"Borwein-Bradley-type identities for Ramanujan-type series for $1/\u03c0^4$","publication_year":2026,"publication_date":"2026-10-03","ids":{"openalex":"https://openalex.org/W7220709447","doi":"https://doi.org/10.48550/arxiv.2610.04770"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04770","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04770","pdf_url":"https://arxiv.org/pdf/2610.04770","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/2610.04770","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120002965","display_name":"Noam Shalev","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shalev, Noam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5120002965"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"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":1.0,"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":0.0,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/ramanujan-type-series","display_name":"Ramanujan-type series","score":0.9980000257492065},{"id":"https://openalex.org/keywords/harmonic-numbers","display_name":"harmonic numbers","score":0.9959999918937683},{"id":"https://openalex.org/keywords/zeta-values","display_name":"zeta values","score":0.8050000071525574}],"concepts":[{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.8064000010490417},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7585999965667725},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7436000108718872},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4691999852657318},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4546000063419342},{"id":"https://openalex.org/C184311908","wikidata":"https://www.wikidata.org/wiki/Q425432","display_name":"Laurent series","level":2,"score":0.428600013256073},{"id":"https://openalex.org/C195597517","wikidata":"https://www.wikidata.org/wiki/Q438842","display_name":"Alternating series","level":3,"score":0.41370001435279846},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40950000286102295},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.4018999934196472},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.37940001487731934},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3531999886035919},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2734000086784363},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C1115519","wikidata":"https://www.wikidata.org/wiki/Q1211057","display_name":"Convergent series","level":3,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04770","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04770","pdf_url":"https://arxiv.org/pdf/2610.04770","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.2610.04770","doi":"https://doi.org/10.48550/arxiv.2610.04770","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04770","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.04770","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04770","pdf_url":"https://arxiv.org/pdf/2610.04770","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220709447.pdf","grobid_xml":"https://content.openalex.org/works/W7220709447.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1801105578","https://openalex.org/W2041457691","https://openalex.org/W2536965463","https://openalex.org/W3126860935","https://openalex.org/W4383605109","https://openalex.org/W4387436664","https://openalex.org/W4392617455","https://openalex.org/W4405734898","https://openalex.org/W4406902512","https://openalex.org/W4407808321","https://openalex.org/W4409898013","https://openalex.org/W6967266735","https://openalex.org/W7128488718","https://openalex.org/W7171982973"],"related_works":["https://openalex.org/W2952083352","https://openalex.org/W1975215860","https://openalex.org/W2950256035","https://openalex.org/W4392618013","https://openalex.org/W4406902512","https://openalex.org/W4319072524","https://openalex.org/W68552308","https://openalex.org/W4385753009","https://openalex.org/W7147105758","https://openalex.org/W4394665044"],"abstract_inverted_index":{"We":[0,50],"prove":[1],"ten":[2],"conjectures":[3],"of":[4,43,46,76,90,93,106],"Z.-W.":[5],"Sun":[6],"on":[7,31],"Ramanujan-type":[8],"series":[9,45,103],"for":[10,104],"$1/\u03c0^4$":[11],"and":[12,48,61,72,96],"$\u03c0^4$":[13],"with":[14],"harmonic":[15],"numbers.":[16],"They":[17],"follow":[18],"by":[19],"comparing":[20],"Taylor":[21,99],"coefficients":[22,100],"in":[23],"new":[24,74],"Borwein-Bradley-type":[25],"identities,":[26],"whose":[27,98],"products":[28,105],"depend":[29],"only":[30],"$x^3$,":[32],"$x^4$,":[33],"$x^6$":[34],"or":[35],"$x^8$.":[36],"These":[37],"identities":[38,92],"come":[39],"from":[40,54],"parametric":[41],"extensions":[42,53],"the":[44,52,77,81,91],"Cullen":[47],"Zhao.":[49],"derive":[51],"K.":[55],"C.":[56],"Au's":[57],"Wilf-Zeilberger":[58],"(WZ)":[59],"seeds,":[60],"their":[62],"sums":[63],"are":[64,101],"trigonometric.":[65],"Our":[66],"proofs":[67,75],"use":[68],"Guillera's":[69],"periodicity":[70],"argument":[71],"give":[73],"original":[78],"series.":[79],"In":[80],"same":[82],"way,":[83],"Dougall's":[84],"$_5F_4$":[85],"sum":[86],"gives":[87],"half-integer":[88],"analogues":[89],"Koecher,":[94],"Borwein-Bradley":[95],"Cohen,":[97],"Ap\u00e9ry-like":[102],"zeta":[107],"values.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
