{"id":"https://openalex.org/W7204234114","doi":"https://doi.org/10.48550/arxiv.2608.24719","title":"Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups","display_name":"Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204234114","doi":"https://doi.org/10.48550/arxiv.2608.24719"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.24719","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24719","pdf_url":"https://arxiv.org/pdf/2608.24719","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/2608.24719","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148242484","display_name":"Alan Xuelun Hou","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hou, Alan Xuelun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046742770","display_name":"Yusheng Lei","orcid":"https://orcid.org/0000-0002-5155-4666","observed_orcids":["https://orcid.org/0000-0002-5155-4666"]},"institutions":[{"id":"https://openalex.org/I6902469","display_name":"Brandeis University","ror":"https://ror.org/05abbep66","country_code":"US","type":"education","lineage":["https://openalex.org/I6902469"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lei, Yusheng","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , BRANDEIS UNIVERSITY , WALTHAM , MASSACHUSETTS , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , BRANDEIS UNIVERSITY , WALTHAM , MASSACHUSETTS , USA","institution_ids":["https://openalex.org/I6902469"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T11680","display_name":"Advanced Algebra and Geometry","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/T11680","display_name":"Advanced Algebra and Geometry","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/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/symplectic-group","display_name":"symplectic group","score":0.996999979019165},{"id":"https://openalex.org/keywords/fourier-coefficients","display_name":"Fourier coefficients","score":0.9359999895095825},{"id":"https://openalex.org/keywords/holomorphic-sections","display_name":"holomorphic sections","score":0.8560000061988831}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8155999779701233},{"id":"https://openalex.org/C133835828","wikidata":"https://www.wikidata.org/wiki/Q1313257","display_name":"Eisenstein series","level":3,"score":0.796999990940094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7961000204086304},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.7268999814987183},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6888999938964844},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5745999813079834},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.5685999989509583},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.4618000090122223},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4478999972343445},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C132817261","wikidata":"https://www.wikidata.org/wiki/Q1134435","display_name":"Automorphic form","level":2,"score":0.4300000071525574},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.40959998965263367},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3822000026702881},{"id":"https://openalex.org/C127559803","wikidata":"https://www.wikidata.org/wiki/Q5161149","display_name":"Conjugate Fourier series","level":5,"score":0.3118000030517578},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.311599999666214},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.3052000105381012},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2953000068664551},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.25949999690055847},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.24719","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24719","pdf_url":"https://arxiv.org/pdf/2608.24719","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.2608.24719","doi":"https://doi.org/10.48550/arxiv.2608.24719","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.24719","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:2608.24719","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24719","pdf_url":"https://arxiv.org/pdf/2608.24719","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/W7204234114.pdf","grobid_xml":"https://content.openalex.org/works/W7204234114.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1924656052","https://openalex.org/W2604421448","https://openalex.org/W7117425622","https://openalex.org/W1648868162","https://openalex.org/W7096086680","https://openalex.org/W2278325608","https://openalex.org/W2133571299","https://openalex.org/W2967594884","https://openalex.org/W3168286586","https://openalex.org/W2013068292"],"abstract_inverted_index":{"We":[0,14,39,78],"study":[1],"degenerate":[2],"Eisenstein":[3,31,92],"series":[4,32],"on":[5],"symplectic":[6,26],"groups":[7],"and":[8,52,72],"construct":[9],"a":[10,17,24],"new":[11],"automorphic":[12],"descent.":[13],"show":[15],"that":[16],"certain":[18],"Fourier":[19,89],"coefficient,":[20],"after":[21],"restriction":[22],"to":[23,87],"smaller":[25],"group,":[27],"is":[28],"itself":[29],"an":[30,81],"with":[33],"the":[34,41,49,63,84],"same":[35],"inducing":[36],"parameter":[37],"\\(s\\).":[38],"describe":[40],"resulting":[42],"holomorphic":[43],"section":[44,51],"explicitly":[45],"in":[46],"terms":[47],"of":[48,62,83,91],"original":[50],"local":[53,64],"\\(L\\)-factors":[54],"at":[55,69,75],"unramified":[56],"places.":[57,77],"At":[58],"every":[59],"regular":[60],"point":[61],"descent,":[65],"we":[66],"prove":[67],"surjectivity":[68],"non-Archimedean":[70],"places":[71],"dense":[73],"image":[74],"Archimedean":[76],"finally":[79],"indicate":[80],"application":[82],"iterated":[85],"descent":[86],"maximal":[88],"coefficients":[90],"series.":[93]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-27T00:00:00"}