{"id":"https://openalex.org/W7222932837","doi":"https://doi.org/10.48550/arxiv.2610.22933","title":"A Criterion for Finite Hypergeometric Reductions of Lauricella's $F_C$ with Arguments Related by Cube Roots of Unity","display_name":"A Criterion for Finite Hypergeometric Reductions of Lauricella's $F_C$ with Arguments Related by Cube Roots of Unity","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222932837","doi":"https://doi.org/10.48550/arxiv.2610.22933"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.22933","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22933","pdf_url":"https://arxiv.org/pdf/2610.22933","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/2610.22933","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051914596","display_name":"Ryunosuke NAKANO","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nakano, Ryunosuke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5051914596"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.913100004196167,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.913100004196167,"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"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.07620000094175339,"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":0.0015999999595806003,"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/lauricella-hypergeometric-function","display_name":"Lauricella hypergeometric function","score":0.7630000114440918},{"id":"https://openalex.org/keywords/cube-roots-of-unity","display_name":"cube roots of unity","score":0.8370000123977661},{"id":"https://openalex.org/keywords/generalized-hypergeometric-series","display_name":"generalized hypergeometric series","score":0.9179999828338623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9190999865531921},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6118999719619751},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5900999903678894},{"id":"https://openalex.org/C155568369","wikidata":"https://www.wikidata.org/wiki/Q1428097","display_name":"Radius of convergence","level":3,"score":0.5174000263214111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49889999628067017},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.4300000071525574},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42750000953674316},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42669999599456787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41749998927116394},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31709998846054077},{"id":"https://openalex.org/C16757182","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Power function","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.22933","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22933","pdf_url":"https://arxiv.org/pdf/2610.22933","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.2610.22933","doi":"https://doi.org/10.48550/arxiv.2610.22933","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.22933","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:2610.22933","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22933","pdf_url":"https://arxiv.org/pdf/2610.22933","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/W7222932837.pdf","grobid_xml":"https://content.openalex.org/works/W7222932837.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2010766012","https://openalex.org/W2036743822","https://openalex.org/W2048563120","https://openalex.org/W2260682791","https://openalex.org/W2963260406"],"related_works":["https://openalex.org/W1985765221","https://openalex.org/W2039910938","https://openalex.org/W2039214402","https://openalex.org/W3085973377","https://openalex.org/W4389920824","https://openalex.org/W2286168187","https://openalex.org/W4315434461","https://openalex.org/W2554829775","https://openalex.org/W2083567415","https://openalex.org/W7215182777"],"abstract_inverted_index":{"We":[0,13,26,77,110],"consider":[1,27],"the":[2,5,67,73,121,125],"germ":[3],"at":[4,134],"origin":[6,74],"of":[7,31,58,102,117,124],"Lauricella's":[8],"function":[9],"$F_C^{(3)}(a,b;c_0,c_1,c_2;\u03ba,\u03c9\u03ba,\u03c9^2\u03ba)$,":[10],"where":[11,39],"$\u03c9=\\exp(2\u03c0\\sqrt{-1}/3)$.":[12],"assume":[14],"that":[15,21,46,79],"$a,b,c_0,c_1,c_2$":[16],"avoid":[17,24],"nonpositive":[18,68],"integers":[19,69],"and":[20,70,85,98,129],"$c_0,c_1,c_2$":[22],"also":[23],"half-integers.":[25],"finite":[28,100],"linear":[29],"combinations":[30],"ordinary":[32,103],"generalized":[33],"hypergeometric":[34],"series":[35,62],"with":[36],"arguments":[37],"$\u03b1\u03ba^3$,":[38],"$\u03b1$":[40],"is":[41,95],"a":[42,54,81],"nonzero":[43],"complex":[44],"constant":[45],"may":[47],"vary":[48],"between":[49],"summands,":[50],"each":[51,89],"multiplied":[52],"by":[53],"nonnegative":[55],"integer":[56],"power":[57],"$\u03ba$.":[59],"Every":[60],"target":[61],"has":[63],"lower":[64],"parameters":[65],"outside":[66],"converges":[71],"near":[72],"or":[75,93],"terminates.":[76],"prove":[78,111],"such":[80],"representation":[82],"exists":[83],"if":[84],"only":[86],"if,":[87],"for":[88,120],"$j=0,1,2$,":[90],"either":[91],"$c_j-c_0$":[92],"$c_j+c_0$":[94],"an":[96],"integer,":[97],"construct":[99],"sums":[101],"${}_9F_8$":[104],"functions":[105,123],"when":[106],"this":[107],"condition":[108],"holds.":[109],"necessity":[112],"from":[113,130],"irreducible":[114],"differential":[115],"equations":[116],"order":[118],"$24$":[119],"generating":[122],"three":[126],"coefficient":[127],"subsequences":[128],"their":[131],"formal":[132],"solutions":[133],"infinity.":[135]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-20T00:00:00"}