{"id":"https://openalex.org/W7213317645","doi":"https://doi.org/10.48550/arxiv.2609.13932","title":"Density of Vanishing of Certain Eigenspaces of Cyclotomic Class Groups","display_name":"Density of Vanishing of Certain Eigenspaces of Cyclotomic Class Groups","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213317645","doi":"https://doi.org/10.48550/arxiv.2609.13932"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13932","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13932","pdf_url":"https://arxiv.org/pdf/2609.13932","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/2609.13932","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151707460","display_name":"Xuejun Guo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Xuejun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004745198","display_name":"Zhengyu Tao","orcid":"https://orcid.org/0000-0002-2884-6732","observed_orcids":["https://orcid.org/0000-0002-2884-6732"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao, Zhengyu","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/T11166","display_name":"Analytic Number Theory Research","score":0.7343999743461609,"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/T11166","display_name":"Analytic Number Theory Research","score":0.7343999743461609,"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":0.2093999981880188,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.010099999606609344,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/eigenspaces","display_name":"eigenspaces","score":0.6029999852180481},{"id":"https://openalex.org/keywords/limiting-laws","display_name":"limiting laws","score":0.6679999828338623},{"id":"https://openalex.org/keywords/reflection-formula","display_name":"reflection formula","score":0.3880000114440918},{"id":"https://openalex.org/keywords/prime-density","display_name":"prime density","score":0.43799999356269836},{"id":"https://openalex.org/keywords/roots-of-unity","display_name":"roots of unity","score":0.6740000247955322}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9162999987602234},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6132000088691711},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5946000218391418},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5719000101089478},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5552999973297119},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5372999906539917},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5206999778747559},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4611999988555908},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4431999921798706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4009999930858612},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.3513999879360199},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31189998984336853},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13932","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13932","pdf_url":"https://arxiv.org/pdf/2609.13932","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.2609.13932","doi":"https://doi.org/10.48550/arxiv.2609.13932","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13932","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:2609.13932","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13932","pdf_url":"https://arxiv.org/pdf/2609.13932","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":[{"id":"https://openalex.org/G8842371449","display_name":null,"funder_award_id":"12231009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213317645.pdf","grobid_xml":"https://content.openalex.org/works/W7213317645.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1703119562","https://openalex.org/W1967150711","https://openalex.org/W1978375108","https://openalex.org/W1991175723","https://openalex.org/W1993224651","https://openalex.org/W2015670049","https://openalex.org/W2015760370","https://openalex.org/W2950392381","https://openalex.org/W2963256112","https://openalex.org/W2963621804","https://openalex.org/W4292101538","https://openalex.org/W4413065475","https://openalex.org/W4416571045","https://openalex.org/W7167089983"],"related_works":["https://openalex.org/W1703119562","https://openalex.org/W4364361594","https://openalex.org/W2973142465","https://openalex.org/W2079194946","https://openalex.org/W2963256112","https://openalex.org/W2557741897","https://openalex.org/W6967108782","https://openalex.org/W2529984020","https://openalex.org/W4210609120","https://openalex.org/W1993224651"],"abstract_inverted_index":{"For":[0,30,66,92],"an":[1,19,131],"odd":[2,43,96,159],"prime":[3,160],"$p$,":[4],"let":[5,26],"$A_j$":[6],"be":[7],"the":[8,11,42,56,83,95,111,145,167],"$\u03c9^j$-eigenspace":[9],"of":[10,15,35,77,108,137,141],"$p$-primary":[12],"class":[13],"group":[14],"$\\mathbb":[16],"Q(\u03b6_p)$.":[17],"Fix":[18],"even":[20,57,84],"integer":[21],"$d\\ge4$,":[22],"put":[23],"$N=(p-1)/d$,":[24],"and":[25,52,149],"$U_d=(\\mathbb":[27],"Z/d\\mathbb":[28],"Z)^\\times$.":[29],"a":[31,73,104,162],"relative":[32,74,105,146],"density-one":[33,75,106],"set":[34,76,107],"primes":[36,78,109],"$p\\equiv":[37,79],"d+1\\pmod{2d}$,":[38],"we":[39],"prove":[40],"that":[41,55],"block":[44,58,97],"$\\bigoplus_{a\\in":[45,59],"U_d}A_{aN}$":[46],"has":[47,61,98],"order":[48,99],"at":[49,63,100],"most":[50,64,101],"$p^{\u03c6(d)/2-1}$,":[51],"reflection":[53],"shows":[54],"U_d}A_{p-aN}$":[60],"$p$-rank":[62],"$\u03c6(d)/2-1$.":[65],"each":[67,93],"$d\\in\\{4,6\\}$,":[68],"both":[69],"blocks":[70],"vanish":[71,86],"for":[72,103,135,157],"d+1\\pmod{2d}$;":[80],"in":[81,87,110,122],"particular,":[82],"components":[85],"accordance":[88,123],"with":[89,124],"Vandiver's":[90],"conjecture.":[91,127],"$d\\in\\{8,10,12\\}$,":[94],"$p$":[102],"same":[112],"progression,":[113],"so":[114],"every":[115,158],"summand":[116],"$A_{aN}$,":[117],"$a\\in":[118],"U_d$,":[119],"is":[120],"cyclic,":[121],"Iwasawa's":[125],"cyclicity":[126],"The":[128],"proof":[129],"uses":[130],"atomless":[132],"limiting":[133],"law":[134],"products":[136],"Dirichlet":[138],"$L$-values,":[139],"integrality":[140],"generalized":[142],"Bernoulli":[143],"norms,":[144],"class-number":[147],"formula":[148],"reflection.":[150],"A":[151],"separate":[152],"exact":[153],"computation":[154],"proves":[155],"$A_{34}=0$":[156],"$p$;":[161],"single-file":[163],"PARI/GP":[164],"program":[165],"reproduces":[166],"calculation.":[168]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
