{"id":"https://openalex.org/W7204473583","doi":"https://doi.org/10.48550/arxiv.2608.26007","title":"An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms","display_name":"An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204473583","doi":"https://doi.org/10.48550/arxiv.2608.26007"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.26007","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26007","pdf_url":"https://arxiv.org/pdf/2608.26007","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/2608.26007","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000644640","display_name":"Biplab Paul","orcid":"https://orcid.org/0000-0001-6658-1758","observed_orcids":["https://orcid.org/0000-0001-6658-1758"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul, Biplab","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033667445","display_name":"Ameya Pitale","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pitale, Ameya","raw_affiliation_strings":["Department of Mathematics , University of North Texas , Denton , TX 76203 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of North Texas , Denton , TX 76203 , USA","institution_ids":["https://openalex.org/I123534392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028120984","display_name":"Abhishek Saha","orcid":"https://orcid.org/0000-0002-2867-0386","observed_orcids":["https://orcid.org/0000-0002-2867-0386"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saha, Abhishek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138613277","display_name":"Ralf Schmidt","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmidt, Ralf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"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":0.9990000128746033,"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":0.9990000128746033,"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":0.000699999975040555,"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":9.999999747378752e-05,"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/petersson-norm","display_name":"Petersson norm","score":0.7450000047683716},{"id":"https://openalex.org/keywords/modular-forms-of-half-integral-weight","display_name":"half-integral weight modular forms","score":0.9240000247955322},{"id":"https://openalex.org/keywords/fourier-coefficients","display_name":"Fourier coefficients","score":0.7720000147819519},{"id":"https://openalex.org/keywords/central-l-values","display_name":"central L-values","score":0.8420000076293945}],"concepts":[{"id":"https://openalex.org/C2778400075","wikidata":"https://www.wikidata.org/wiki/Q655275","display_name":"Cusp (singularity)","level":2,"score":0.8740000128746033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8709999918937683},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.7542999982833862},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7516999840736389},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6876000165939331},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6230999827384949},{"id":"https://openalex.org/C2214281","wikidata":"https://www.wikidata.org/wiki/Q7510567","display_name":"Siegel modular form","level":3,"score":0.46630001068115234},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30820000171661377},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.29510000348091125},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26350000500679016}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.26007","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26007","pdf_url":"https://arxiv.org/pdf/2608.26007","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.2608.26007","doi":"https://doi.org/10.48550/arxiv.2608.26007","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.26007","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:2608.26007","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26007","pdf_url":"https://arxiv.org/pdf/2608.26007","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/W7204473583.pdf","grobid_xml":"https://content.openalex.org/works/W7204473583.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2800229961","https://openalex.org/W7118423329"],"related_works":["https://openalex.org/W2407788570","https://openalex.org/W2577572455","https://openalex.org/W2787992528","https://openalex.org/W2885456048","https://openalex.org/W2053613200","https://openalex.org/W1925290474","https://openalex.org/W4408385242","https://openalex.org/W4379140860","https://openalex.org/W2216893620","https://openalex.org/W2012726188"],"abstract_inverted_index":{"We":[0,43],"compute":[1],"the":[2,7,50,55],"local":[3],"integrals":[4],"appearing":[5],"in":[6,16],"refined":[8],"Gan--Gross--Prasad":[9],"conjecture":[10],"for":[11,49],"Fourier--Jacobi":[12],"periods":[13],"of":[14,32,46,52,57,62],"$\\mathrm{Sp}_4$":[15],"new":[17],"ramified":[18],"cases":[19],"and":[20,38,60],"use":[21],"this":[22],"to":[23],"formulate":[24],"an":[25],"explicit":[26],"conjectural":[27],"identity":[28,48],"relating":[29],"Petersson":[30,53],"norms":[31],"degree":[33],"2":[34],"Siegel":[35],"cusp":[36],"forms":[37],"associated":[39],"half-integral":[40],"weight":[41],"forms.":[42],"note":[44],"consequences":[45],"our":[47],"growth":[51],"norms,":[54],"size":[56],"Fourier":[58],"coefficients,":[59],"non-vanishing":[61],"central":[63],"$L$-values.":[64]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-28T00:00:00"}