{"id":"https://openalex.org/W7223833769","doi":"https://doi.org/10.48550/arxiv.2610.33249","title":"Two parametric $q$-supercongruences from Andrews' multi-series transformation","display_name":"Two parametric $q$-supercongruences from Andrews' multi-series transformation","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223833769","doi":"https://doi.org/10.48550/arxiv.2610.33249"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33249","pdf_url":"https://arxiv.org/pdf/2610.33249","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/2610.33249","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":true,"raw_author_name":"Karmakar, Liton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5117642939"],"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/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/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":0.9419999718666077},{"id":"https://openalex.org/keywords/supercongruences","display_name":"supercongruences","score":0.8259999752044678},{"id":"https://openalex.org/keywords/q-analogues","display_name":"q-analogues","score":0.7480000257492065},{"id":"https://openalex.org/keywords/creative-microscoping","display_name":"creative microscoping","score":0.7269999980926514},{"id":"https://openalex.org/keywords/hypergeometric-series","display_name":"hypergeometric series","score":0.7369999885559082},{"id":"https://openalex.org/keywords/pochhammer-symbol","display_name":"Pochhammer symbol","score":0.7459999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7343000173568726},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5925999879837036},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5184999704360962},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4253999888896942},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4180999994277954},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37389999628067017},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31130000948905945},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.27799999713897705}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.33249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33249","pdf_url":"https://arxiv.org/pdf/2610.33249","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.2610.33249","doi":"https://doi.org/10.48550/arxiv.2610.33249","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33249","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:2610.33249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33249","pdf_url":"https://arxiv.org/pdf/2610.33249","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/W7223833769.pdf","grobid_xml":"https://content.openalex.org/works/W7223833769.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7214276392","https://openalex.org/W7168351265","https://openalex.org/W4417246633","https://openalex.org/W7172419609","https://openalex.org/W4409708280","https://openalex.org/W3129139660","https://openalex.org/W7221137834","https://openalex.org/W7160863944","https://openalex.org/W2204652060","https://openalex.org/W4407836730"],"abstract_inverted_index":{"Recently,":[0],"Guo":[1,3,18,88],"and":[2,19,23,89,92],"(Results":[4],"Math":[5],"$76:37,":[6],"~2021$)":[7],"obtained":[8],"curious":[9],"$q$-analogues":[10],"of":[11,73,78],"the":[12,62,82],"following":[13],"two":[14],"supercongruences":[15],"conjectured":[16],"by":[17,87],"Schlosser":[20],"\\cite[Conjectures":[21],"$12.6$":[22],"$12.7$]{GuoSclssr":[24],"ConstApprox":[25],"21}:":[26],"\\begin{align*}":[27,43],"\\sum_{n=0}^{(p-1)/3}":[28],"(6n+1)":[29],"\\frac{\\left(\\frac{1}{3}\\right)_n^{4}(2n)!}":[30],"{(n!)^{4}\\left(\\frac{2}{3}\\right)_{2n}}":[31],"\\equiv":[32,48],"p":[33,49],"\\pmod{p^{3}}":[34,50],"\\qquad":[35,51],"\\text{for":[36,52],"primes":[37,53],"}":[38,54],"p\\equiv":[39,55],"1":[40],"\\pmod{3},":[41,57],"\\end{align*}":[42,58],"\\sum_{n=0}^{(p+1)/3}":[44],"(6n-1)":[45],"\\frac{\\left(-\\frac{1}{3}\\right)_n^{4}(2n)!}":[46],"{(n!)^{4}\\left(-\\frac{2}{3}\\right)_{2n}}":[47],"2":[56],"where":[59],"$(z)_n=z(z+1)\\cdots(z+n-1)$":[60],"denotes":[61],"shifted":[63],"factorial.":[64],"In":[65],"this":[66],"paper,":[67],"we":[68],"establish":[69],"a":[70],"one-parameter":[71],"extension":[72],"them.":[74],"The":[75],"main":[76],"ingredients":[77],"our":[79],"proofs":[80],"are":[81],"creative":[83],"microscoping":[84],"method":[85],"developed":[86],"Zudilin":[90],"\\cite{guo2019q}":[91],"Andrews'":[93],"multi-series":[94],"transformation.":[95]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-28T00:00:00"}
