{"id":"https://openalex.org/W7213508604","doi":"https://doi.org/10.48550/arxiv.2609.18220","title":"Nonvanishing of ray class $L$-functions","display_name":"Nonvanishing of ray class $L$-functions","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213508604","doi":"https://doi.org/10.48550/arxiv.2609.18220"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18220","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18220","pdf_url":"https://arxiv.org/pdf/2609.18220","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/2609.18220","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152028010","display_name":"Thurman Ye","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ye, Thurman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5151998223","display_name":"Xu Zhuang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhuang, Xu","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":0.9955999851226807,"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":0.9955999851226807,"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":0.003700000001117587,"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":0.0,"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/imaginary-quadratic-fields","display_name":"imaginary quadratic fields","score":0.9120000004768372},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"asymptotic formula","score":0.8059999942779541},{"id":"https://openalex.org/keywords/dirichlet-l-functions","display_name":"Dirichlet L-functions","score":0.6759999990463257}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7713000178337097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7095999717712402},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6601999998092651},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5446000099182129},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4961000084877014},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4887000024318695},{"id":"https://openalex.org/C195831351","wikidata":"https://www.wikidata.org/wiki/Q1744580","display_name":"Class field theory","level":3,"score":0.3490000069141388},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C2776020190","wikidata":"https://www.wikidata.org/wiki/Q997453","display_name":"New class","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2930999994277954},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18220","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18220","pdf_url":"https://arxiv.org/pdf/2609.18220","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.2609.18220","doi":"https://doi.org/10.48550/arxiv.2609.18220","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18220","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:2609.18220","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18220","pdf_url":"https://arxiv.org/pdf/2609.18220","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":[{"id":"https://openalex.org/F4320322675","display_name":"Mitacs","ror":"https://ror.org/00cjrc276"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213508604.pdf","grobid_xml":"https://content.openalex.org/works/W7213508604.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4416542302"],"related_works":["https://openalex.org/W7140185570","https://openalex.org/W2323102738","https://openalex.org/W3044866995","https://openalex.org/W2032381467","https://openalex.org/W2796307977","https://openalex.org/W4416542302","https://openalex.org/W7223156235","https://openalex.org/W3196513931","https://openalex.org/W4389513996","https://openalex.org/W2944806985"],"abstract_inverted_index":{"We":[0,18],"study":[1],"the":[2,33,48,53,62],"nonvanishing":[3],"of":[4,7,32],"central":[5],"values":[6],"ray":[8,35,54],"class":[9,36,55],"$L$-functions":[10],"over":[11],"a":[12,29],"fixed":[13],"imaginary":[14],"quadratic":[15],"field":[16],"$K$.":[17],"prove":[19],"that,":[20],"as":[21],"$\\mathrm{N}(\\mathfrak":[22],"f)$":[23],"tends":[24],"to":[25,52],"infinity,":[26],"at":[27],"least":[28],"proportion":[30],"$1/3-\\mathsf{o}_K(1)$":[31],"primitive":[34],"characters":[37],"$\u03c7$":[38],"modulo":[39],"$\\mathfrak":[40],"f$":[41],"satisfy":[42],"$L(1/2,\u03c7)\\neq":[43],"0$.":[44],"Our":[45],"proof":[46],"adapts":[47],"classical":[49],"mollifier":[50],"method":[51],"setting":[56],"and":[57,64],"establishes":[58],"asymptotic":[59],"formulas":[60],"for":[61],"first":[63],"second":[65],"mollified":[66],"moments.":[67]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}