{"id":"https://openalex.org/W7221084875","doi":"https://doi.org/10.48550/arxiv.2610.11778","title":"$q$-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial","display_name":"$q$-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7221084875","doi":"https://doi.org/10.48550/arxiv.2610.11778"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.11778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11778","pdf_url":"https://arxiv.org/pdf/2610.11778","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/2610.11778","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117642939","display_name":"Liton Karmakar","orcid":"https://orcid.org/0009-0002-9532-1677","observed_orcids":["https://orcid.org/0009-0002-9532-1677"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karmakar, Liton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010201668","display_name":"Arijit Jana","orcid":"https://orcid.org/0000-0002-7440-3297","observed_orcids":["https://orcid.org/0000-0002-7440-3297"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jana, Arijit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/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/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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0,"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/q-supercongruences","display_name":"q-supercongruences","score":0.996999979019165},{"id":"https://openalex.org/keywords/basic-hypergeometric-series","display_name":"basic hypergeometric series","score":0.9010000228881836},{"id":"https://openalex.org/keywords/cyclotomic-polynomials","display_name":"cyclotomic polynomials","score":0.9610000252723694},{"id":"https://openalex.org/keywords/creative-microscoping","display_name":"creative microscoping","score":0.925000011920929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8097000122070312},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7006999850273132},{"id":"https://openalex.org/C76253118","wikidata":"https://www.wikidata.org/wiki/Q1051983","display_name":"Cyclotomic polynomial","level":3,"score":0.6326000094413757},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5533000230789185},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42590001225471497},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.40560001134872437},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37400001287460327},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C60400383","wikidata":"https://www.wikidata.org/wiki/Q17028407","display_name":"Hypergeometric identity","level":5,"score":0.35019999742507935},{"id":"https://openalex.org/C92941272","wikidata":"https://www.wikidata.org/wiki/Q1062958","display_name":"Basic hypergeometric series","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.29820001125335693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2980000078678131},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2825999855995178},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.25529998540878296}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.11778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11778","pdf_url":"https://arxiv.org/pdf/2610.11778","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.2610.11778","doi":"https://doi.org/10.48550/arxiv.2610.11778","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.11778","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:2610.11778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11778","pdf_url":"https://arxiv.org/pdf/2610.11778","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/W7221084875.pdf","grobid_xml":"https://content.openalex.org/works/W7221084875.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3213417290","https://openalex.org/W7125412547","https://openalex.org/W4409708280","https://openalex.org/W4310022255","https://openalex.org/W3153729552","https://openalex.org/W4402427619","https://openalex.org/W7164005285","https://openalex.org/W7213455968","https://openalex.org/W4283688863","https://openalex.org/W4390829971"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"establish":[4],"several":[5,24],"$q$-supercongruences":[6],"for":[7],"basic":[8],"hypergeometric":[9],"series":[10],"modulo":[11],"the":[12,29,40],"third":[13],"and":[14,31,47],"fifth":[15],"powers":[16],"of":[17,34],"a":[18],"cyclotomic":[19],"polynomial.":[20],"These":[21],"results":[22],"extend":[23],"existing":[25],"supercongruences":[26,33],"related":[27],"to":[28],"$\\mathrm{(A.2)}$":[30],"$\\mathrm{(C.2)}$":[32],"Van":[35],"Hamme.":[36],"Our":[37],"proofs":[38],"employ":[39],"creative":[41],"microscoping":[42],"method":[43],"developed":[44],"by":[45],"Guo":[46],"Zudilin":[48],"\\cite{guo2019q},":[49],"together":[50],"with":[51],"Watson's":[52],"${}_{8}\u03d5_7$":[53],"transformation":[54],"formula.":[55]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-10T00:00:00"}
