{"id":"https://openalex.org/W4385066477","doi":"https://doi.org/10.1080/10586458.2023.2219071","title":"Higher Rademacher Symbols","display_name":"Higher Rademacher Symbols","publication_year":2023,"publication_date":"2023-07-21","ids":{"openalex":"https://openalex.org/W4385066477","doi":"https://doi.org/10.1080/10586458.2023.2219071"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2023.2219071","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2023.2219071","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008974653","display_name":"William Duke","orcid":null},"institutions":[{"id":"https://openalex.org/I2799798094","display_name":"UCLA Health","ror":"https://ror.org/01d88se56","country_code":"US","type":"funder","lineage":["https://openalex.org/I2799798094"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W. Duke","raw_affiliation_strings":["UCLA Mathematics Department, Los Angeles, CA"],"affiliations":[{"raw_affiliation_string":"UCLA Mathematics Department, Los Angeles, CA","institution_ids":["https://openalex.org/I2799798094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008974653"],"corresponding_institution_ids":["https://openalex.org/I2799798094"],"apc_list":null,"apc_paid":null,"fwci":1.0957,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.70935807,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"33","issue":"4","first_page":"624","last_page":"643"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9400687217712402},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.6253156661987305},{"id":"https://openalex.org/keywords/arithmetic-zeta-function","display_name":"Arithmetic zeta function","score":0.5919706225395203},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.5691640377044678},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5439798831939697},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5226823687553406},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5065926313400269},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.4887106418609619},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4865240454673767},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.4788206219673157},{"id":"https://openalex.org/keywords/prime-zeta-function","display_name":"Prime zeta function","score":0.47340235114097595},{"id":"https://openalex.org/keywords/quadratic-field","display_name":"Quadratic field","score":0.46333399415016174},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.461535781621933},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45415109395980835},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4473153054714203},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37876176834106445},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.20097684860229492}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9400687217712402},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.6253156661987305},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"score":0.5919706225395203},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.5691640377044678},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5439798831939697},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5226823687553406},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5065926313400269},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.4887106418609619},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4865240454673767},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.4788206219673157},{"id":"https://openalex.org/C71897612","wikidata":"https://www.wikidata.org/wiki/Q1896470","display_name":"Prime zeta function","level":4,"score":0.47340235114097595},{"id":"https://openalex.org/C95136341","wikidata":"https://www.wikidata.org/wiki/Q625519","display_name":"Quadratic field","level":4,"score":0.46333399415016174},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.461535781621933},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45415109395980835},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4473153054714203},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37876176834106445},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.20097684860229492},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2023.2219071","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2023.2219071","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.41999998688697815}],"awards":[{"id":"https://openalex.org/G7506296997","display_name":null,"funder_award_id":"DMS 1701638","funder_id":"https://openalex.org/F4320320373","funder_display_name":"National Stroke Foundation"}],"funders":[{"id":"https://openalex.org/F4320320373","display_name":"National Stroke Foundation","ror":"https://ror.org/004ckc033"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W50969635","https://openalex.org/W106636584","https://openalex.org/W1964281545","https://openalex.org/W1981065777","https://openalex.org/W1988817136","https://openalex.org/W2009873794","https://openalex.org/W2012357945","https://openalex.org/W2018180343","https://openalex.org/W2028369373","https://openalex.org/W2029657122","https://openalex.org/W2032267222","https://openalex.org/W2036343431","https://openalex.org/W2042930695","https://openalex.org/W2043372198","https://openalex.org/W2051013467","https://openalex.org/W2072115727","https://openalex.org/W2089480974","https://openalex.org/W2089501550","https://openalex.org/W2103670885","https://openalex.org/W2147090941","https://openalex.org/W2243586082","https://openalex.org/W2266727805","https://openalex.org/W2495238664","https://openalex.org/W2499325432","https://openalex.org/W2795529709","https://openalex.org/W3120970988","https://openalex.org/W3126984557","https://openalex.org/W3140863823","https://openalex.org/W4230873712","https://openalex.org/W4246014113","https://openalex.org/W4400536925","https://openalex.org/W6629348468","https://openalex.org/W6723780267","https://openalex.org/W6992702995","https://openalex.org/W7053447510"],"related_works":["https://openalex.org/W68100126","https://openalex.org/W4300112600","https://openalex.org/W2962759484","https://openalex.org/W2092502219","https://openalex.org/W869653275","https://openalex.org/W4287183599","https://openalex.org/W3160297915","https://openalex.org/W1637899513","https://openalex.org/W2944854401","https://openalex.org/W2090039434"],"abstract_inverted_index":{"Certain":[0],"higher":[1],"Rademacher":[2,50],"symbols":[3,51],"are":[4,17],"defined":[5,114],"that":[6],"give":[7],"class":[8,66],"functions":[9],"on":[10],"the":[11,30,41,44,47,53,59,92,116],"modular":[12],"group.":[13],"Their":[14],"basic":[15],"properties":[16],"derived":[18],"via":[19],"a":[20,63,68,84,96,100,107],"two-variable":[21],"reformulation":[22,27],"of":[23,32,43,46,58,67,78,94,109],"Eichler-Shimura":[24],"cohomology.":[25],"This":[26,72],"better":[28],"explains":[29],"role":[31],"cycle":[33],"integrals":[34],"and":[35],"also":[36],"yields":[37],"new":[38,85],"results,":[39],"about":[40],"integrality":[42],"values":[45,54,113],"symbols.":[48],"The":[49],"determine":[52],"at":[55,99],"non-positive":[56],"integers":[57],"zeta":[60,97,112],"function":[61,98],"for":[62,91,115],"narrow":[64],"ideal":[65],"real":[69],"quadratic":[70,117],"field.":[71,118],"result":[73],"is":[74,81],"equivalent":[75],"to":[76],"one":[77,105],"Siegel,":[79],"but":[80],"proven":[82],"in":[83],"way":[86],"by":[87],"using":[88],"an":[89],"identity":[90],"value":[93],"such":[95],"positive":[101],"integer":[102],"greater":[103],"than":[104],"as":[106],"sum":[108],"certain":[110],"double":[111]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}