{"id":"https://openalex.org/W7221027473","doi":"https://doi.org/10.48550/arxiv.2610.08633","title":"Local newforms, Pa\u0161k\u016bnas-Stevens Whittaker functions, and explicit test vectors for $\\mathrm{GL}(n)\\times \\mathrm{GL}(n)$","display_name":"Local newforms, Pa\u0161k\u016bnas-Stevens Whittaker functions, and explicit test vectors for $\\mathrm{GL}(n)\\times \\mathrm{GL}(n)$","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7221027473","doi":"https://doi.org/10.48550/arxiv.2610.08633"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08633","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08633","pdf_url":"https://arxiv.org/pdf/2610.08633","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/2610.08633","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093766696","display_name":"Alexandros Groutides","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Groutides, Alexandros","raw_affiliation_strings":["Instituto Matem\u00e1ticas de la Universidad de Sevilla"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto Matem\u00e1ticas de la Universidad de Sevilla","institution_ids":["https://openalex.org/I79238269"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5093766696"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"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/T10849","display_name":"Finite Group Theory Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/integral-representation","display_name":"integral representation","score":0.5419999957084656},{"id":"https://openalex.org/keywords/automorphic-forms","display_name":"automorphic forms","score":0.5600000023841858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9412000179290771},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6054999828338623},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42410001158714294},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3700999915599823},{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.31619998812675476},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2736000120639801}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08633","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08633","pdf_url":"https://arxiv.org/pdf/2610.08633","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.2610.08633","doi":"https://doi.org/10.48550/arxiv.2610.08633","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08633","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:2610.08633","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08633","pdf_url":"https://arxiv.org/pdf/2610.08633","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/W7221027473.pdf","grobid_xml":"https://content.openalex.org/works/W7221027473.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2964025360","https://openalex.org/W2978513042","https://openalex.org/W4226506656","https://openalex.org/W2594392546","https://openalex.org/W1837623393","https://openalex.org/W1598178616","https://openalex.org/W2017769182","https://openalex.org/W7101164523","https://openalex.org/W3100258557","https://openalex.org/W4397021837"],"abstract_inverted_index":{"Recently,":[0],"Girsch-Kurinczuk":[1],"have":[2],"obtained":[3],"new":[4,97],"formulas":[5,73],"for":[6,106],"local":[7],"newforms":[8,105],"in":[9,37,65,101],"depth-zero":[10],"and":[11,90],"minimax":[12],"integral-depth":[13],"cuspidal":[14,108],"representations":[15],"of":[16,20,33,39,60,67,93,103],"$p$-adic":[17],"$\\mathrm{GL}(n)$.":[18],"One":[19],"their":[21,112],"main":[22],"results":[23],"is":[24,115],"an":[25,30,57,75],"averaging":[26,53,88],"formula":[27,54,89],"which":[28],"provides":[29],"integral":[31,58],"representation":[32,59],"the":[34,40,45,61,68],"Whittaker":[35,42,63,69,104],"newform":[36],"terms":[38,66,102],"Pa\u0161k\u016bnas-Stevens":[41,62],"function.":[43],"In":[44],"present":[46],"paper,":[47],"we":[48,85],"first":[49],"prove":[50],"a":[51],"reverse":[52],"by":[55],"establishing":[56],"function":[64],"newform.":[70],"Together,":[71],"these":[72,80],"give":[74,96],"explicit":[76,98],"two-way":[77],"passage":[78],"between":[79],"two":[81],"distinguished":[82],"vectors.":[83],"Finally,":[84],"use":[86],"our":[87],"earlier":[91],"work":[92],"Kurinczuk-Matringe":[94],"to":[95,119],"test":[99],"vectors":[100],"such":[107],"$\\mathrm{GL}(n)\\times\\mathrm{GL}(n)$":[109],"pairs,":[110],"whenever":[111],"Rankin-Selberg":[113],"$L$-factor":[114],"not":[116],"identically":[117],"equal":[118],"$1$.":[120]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}
