{"id":"https://openalex.org/W7221165053","doi":"https://doi.org/10.48550/arxiv.2610.10576","title":"The structure of irreducible cuspidal eta quotients","display_name":"The structure of irreducible cuspidal eta quotients","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7221165053","doi":"https://doi.org/10.48550/arxiv.2610.10576"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10576","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10576","pdf_url":"https://arxiv.org/pdf/2610.10576","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.10576","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081114895","display_name":"Soumya Bhattacharya","orcid":"https://orcid.org/0000-0002-0116-7641","observed_orcids":["https://orcid.org/0000-0002-0116-7641"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bhattacharya, Soumya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5081114895"],"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":0.9726999998092651,"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":0.9726999998092651,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.016300000250339508,"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":0.002899999963119626,"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/eta-quotients","display_name":"eta-quotients","score":0.8560000061988831},{"id":"https://openalex.org/keywords/modular-forms-of-half-integral-weight","display_name":"half-integral weight modular forms","score":0.847000002861023}],"concepts":[{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.9168999791145325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8702999949455261},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.679099977016449},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6299999952316284},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6270999908447266},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3093000054359436},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27140000462532043},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.23489999771118164},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.21729999780654907},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.21410000324249268}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10576","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10576","pdf_url":"https://arxiv.org/pdf/2610.10576","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.2610.10576","doi":"https://doi.org/10.48550/arxiv.2610.10576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10576","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10576","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10576","pdf_url":"https://arxiv.org/pdf/2610.10576","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221165053.pdf","grobid_xml":"https://content.openalex.org/works/W7221165053.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2272439807","https://openalex.org/W2588858924","https://openalex.org/W2267160987","https://openalex.org/W3195574051","https://openalex.org/W3167626166","https://openalex.org/W2892125004","https://openalex.org/W2569162992","https://openalex.org/W3199684288","https://openalex.org/W3100952676","https://openalex.org/W2095723123"],"abstract_inverted_index":{"We":[0,58],"show":[1,101],"that":[2,61,93,102],"an":[3],"ir{\\-}reducible":[4],"cuspidal":[5,71],"eta":[6,37,72,89],"quotient":[7,73],"of":[8,16,27,31,43,55,74,82,85,91],"level~$N$":[9],"is":[10,110],"uniquely":[11,49],"identified":[12,50],"by":[13,52,112],"its":[14],"orders":[15,54],"vanishing":[17,56],"at":[18],"$O((\\log_2":[19],"N)^{r-1})$":[20],"cusps,":[21],"where":[22],"$r$":[23],"denotes":[24],"the":[25,80,86,94,106],"number":[26],"distinct":[28],"prime":[29,45],"divisors":[30],"$N$.":[32],"In":[33],"particular,":[34],"all":[35,63,104],"such":[36],"quotients":[38,90],"which":[39],"are":[40,48],"Fricke":[41],"eigenforms":[42],"a":[44,67],"power":[46],"level,":[47,97],"only":[51],"their":[53],"at~$\\infty$.":[57],"also":[59],"prove":[60],"for":[62,103],"$k\\in\\N$,":[64,105],"there":[65],"exists":[66],"primitive":[68,87],"and":[69],"irreducible":[70],"weight":[75],"$k/2$.":[76],"It":[77],"follows":[78],"from":[79],"exhaustiveness":[81],"Zagier's":[83],"list":[84],"holomorphic":[88],"weight~$1/2$":[92],"1st":[95],"Mersmann":[96,108],"$\\cl{M}_1=12$.":[98],"Here":[99],"we":[100],"$k$-th":[107],"level":[109],"divisible":[111],"$2^{2k}$.":[113]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-10T00:00:00"}
