{"id":"https://openalex.org/W7207713522","doi":"https://doi.org/10.48550/arxiv.2609.01990","title":"Jacquet-Zagier treatment of the beyond endoscopy trace formula for $\\mathrm{GL}_2$","display_name":"Jacquet-Zagier treatment of the beyond endoscopy trace formula for $\\mathrm{GL}_2$","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207713522","doi":"https://doi.org/10.48550/arxiv.2609.01990"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01990","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01990","pdf_url":"https://arxiv.org/pdf/2609.01990","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/2609.01990","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5144127181","display_name":"Pranjal Pandurang Warade","orcid":"https://orcid.org/0009-0001-4289-3914","observed_orcids":["https://orcid.org/0009-0001-4289-3914"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Warade, Pranjal Pandurang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5144127181"],"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":0.9970999956130981,"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":0.9970999956130981,"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":0.0026000000070780516,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/trace-formula","display_name":"trace formula","score":0.8309999704360962},{"id":"https://openalex.org/keywords/eisenstein-series","display_name":"Eisenstein series","score":0.8379999995231628},{"id":"https://openalex.org/keywords/l-functions","display_name":"L-functions","score":0.6589999794960022},{"id":"https://openalex.org/keywords/poisson-summation-formula","display_name":"Poisson summation formula","score":0.9509999752044678},{"id":"https://openalex.org/keywords/meromorphic-continuation","display_name":"meromorphic continuation","score":0.9279999732971191},{"id":"https://openalex.org/keywords/automorphic-forms","display_name":"automorphic forms","score":0.4519999921321869}],"concepts":[{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6809999942779541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6794000267982483},{"id":"https://openalex.org/C64092710","wikidata":"https://www.wikidata.org/wiki/Q387743","display_name":"Poisson summation formula","level":3,"score":0.5672000050544739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42669999599456787},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.42170000076293945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40149998664855957},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3513999879360199},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C8077415","wikidata":"https://www.wikidata.org/wiki/Q2596534","display_name":"Poisson kernel","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C2781338088","wikidata":"https://www.wikidata.org/wiki/Q903495","display_name":"Residue (chemistry)","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.29750001430511475},{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01990","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01990","pdf_url":"https://arxiv.org/pdf/2609.01990","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.2609.01990","doi":"https://doi.org/10.48550/arxiv.2609.01990","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01990","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:2609.01990","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01990","pdf_url":"https://arxiv.org/pdf/2609.01990","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/W7207713522.pdf","grobid_xml":"https://content.openalex.org/works/W7207713522.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7171926471","https://openalex.org/W7161952336","https://openalex.org/W7203669666","https://openalex.org/W4416241452","https://openalex.org/W4414581880","https://openalex.org/W4404088853","https://openalex.org/W4394907096","https://openalex.org/W7171682375","https://openalex.org/W2221661915","https://openalex.org/W4313905102"],"abstract_inverted_index":{"We":[0,75],"begin":[1],"the":[2,5,22,32,36,41,46,57,80,84,90,94],"study":[3],"of":[4,21,83,93,107],"beyond":[6],"endoscopic":[7],"trace":[8,58,73,81],"formula":[9,59],"for":[10],"$\\mathrm{GL}_2$":[11],"over":[12],"$\\mathbb{Q}$":[13],"attached":[14],"to":[15,100],"any":[16],"symmetric":[17],"power":[18],"representation":[19],"$\u03c3_k$":[20],"dual":[23],"group":[24],"$\\mathrm{G}L_2(\\mathbb{C})$.":[25],"For":[26],"an":[27],"adelic":[28],"function":[29],"that":[30,89],"incorporates":[31],"$L$-functions":[33],"$L(s_B,\u03c0,\u03c3_k)$":[34],"through":[35],"basic":[37],"functions":[38],"at":[39,63,110],"all":[40],"finite":[42],"places,":[43],"we":[44],"integrate":[45],"cuspidal":[47],"kernel":[48],"against":[49],"a":[50,61,70,105],"corresponding":[51],"Eisenstein":[52],"series":[53],"$E(g,s)$":[54],"and":[55,87],"realize":[56],"as":[60],"residue":[62],"$s=1$,":[64],"replacing":[65],"Arthur's":[66],"truncation":[67],"operation":[68],"by":[69],"continuously":[71],"deformed":[72],"formula.":[74],"argue":[76],"Poisson":[77],"summation":[78],"on":[79],"variable":[82],"Hitchin-Steinberg":[85],"base":[86],"show":[88],"dominant":[91],"term":[92],"elliptic":[95],"part":[96],"admits":[97],"meromorphic":[98],"continuation":[99],"$\\mathfrak{R}(s_B)":[101],"\\geq":[102],"0$":[103],"with":[104],"pole":[106],"order":[108],"$k$":[109],"$s_B":[111],"=1$.":[112]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-04T00:00:00"}