{"id":"https://openalex.org/W2049455601","doi":"https://doi.org/10.1080/10586458.2007.10129004","title":"A Hardy\u2013Ramanujan Formula for Lie Algebras","display_name":"A Hardy\u2013Ramanujan Formula for Lie Algebras","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2049455601","doi":"https://doi.org/10.1080/10586458.2007.10129004","mag":"2049455601"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2007.10129004","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129004","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/A5048021509","display_name":"Gordon Ritter","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gordon Ritter","raw_affiliation_strings":["Department of Physics, Harvard University, 17 Oxford St., Cambridge, MA 02138"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Harvard University, 17 Oxford St., Cambridge, MA 02138","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048021509"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12629184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"16","issue":"3","first_page":"375","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9995999932289124,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9911999702453613,"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/mathematics","display_name":"Mathematics","score":0.9157200455665588},{"id":"https://openalex.org/keywords/semisimple-lie-algebra","display_name":"Semisimple Lie algebra","score":0.5582820773124695},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.523749828338623},{"id":"https://openalex.org/keywords/affine-lie-algebra","display_name":"Affine Lie algebra","score":0.48385345935821533},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.466136634349823},{"id":"https://openalex.org/keywords/theta-function","display_name":"Theta function","score":0.45521068572998047},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43539857864379883},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4309748411178589},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.42156344652175903},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.4133613109588623},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.366113543510437},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2439858317375183},{"id":"https://openalex.org/keywords/current-algebra","display_name":"Current algebra","score":0.12312692403793335}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9157200455665588},{"id":"https://openalex.org/C2778052762","wikidata":"https://www.wikidata.org/wiki/Q2366896","display_name":"Semisimple Lie algebra","level":5,"score":0.5582820773124695},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.523749828338623},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.48385345935821533},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.466136634349823},{"id":"https://openalex.org/C105546189","wikidata":"https://www.wikidata.org/wiki/Q1154787","display_name":"Theta function","level":2,"score":0.45521068572998047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43539857864379883},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4309748411178589},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.42156344652175903},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.4133613109588623},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.366113543510437},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2439858317375183},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.12312692403793335}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2007.10129004","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129004","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"},{"id":"pmh:oai:CULeuclid:euclid.em/1204928537","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1204928537","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1010.3062","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1010.3062","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Gordon_Ritter/publication/241727580_A_HardyRamanujan_Formula_for_Lie_Algebras/links/5422caeb0cf290c9e3ac95f5.pdf?origin%3Dpublication_detail","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1011.7502","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1011.7502","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Gordon_Ritter/publication/241727580_A_HardyRamanujan_Formula_for_Lie_Algebras/links/5422caeb0cf290c9e3ac95f5.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2017964195","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W2911192957","https://openalex.org/W2094240135","https://openalex.org/W2260169109","https://openalex.org/W4294610457","https://openalex.org/W1766818275","https://openalex.org/W2078450633","https://openalex.org/W2553777924","https://openalex.org/W3177407241","https://openalex.org/W2157136072","https://openalex.org/W3146159182"],"abstract_inverted_index":{"We":[0,19,46,140,186],"study":[1],"certain":[2],"combinatoric":[3],"aspects":[4],"of":[5,8,12,53,79,88,107,122,146,161,183,199],"the":[6,21,25,40,49,83,99,119,143,151,159,176,196,200],"set":[7],"all":[9,162],"unitary":[10],"representations":[11],"a":[13,30,93,132,136,156,165,188],"finite-dimensional":[14],"semisimple":[15],"Lie":[16,44],"algebra":[17],"g.":[18],"interpret":[20],"Hardy\u2013Ramanujan\u2013Rademacher":[22],"formula":[23],"for":[24,65,75,102,210],"integer":[26],"partition":[27],"function":[28,101,157,190],"as":[29,155],"statement":[31],"about":[32],"su":[33,211],"2,":[34],"and":[35,115,126,168,203],"explore":[36],"in":[37,55,150,164,179],"some":[38],"detail":[39],"generalization":[41],"to":[42,175,194],"other":[43,76],"algebras.":[45],"conjecture":[47],"that":[48,91,130,191,206],"number":[50,145],"Mod(g,":[51,103],"d)":[52,87,110],"g-modules":[54,90,163],"dimension":[56],"d":[57,66,112,123],"is":[58,96,113,173,192,208],"given":[59,137],"by":[60,98],"(\u03b1/d)":[61],"exp(\u03b2d":[62],"\u03b3":[63],")":[64],"\u00bb":[67],"1,":[68],"which":[69],"(if":[70],"true)":[71],"has":[72],"profound":[73],"consequences":[74],"combinatorial":[77],"invariants":[78],"g-modules.":[80],"In":[81],"particular,":[82],"fraction":[84],"F":[85,108],"1(g,":[86,109],"d-dimensional":[89],"have":[92],"one-dimensional":[94],"submodule":[95],"determined":[97],"generating":[100,128],"d).":[104],"The":[105],"dependence":[106],"on":[111,118,127,158],"complicated":[114],"beautiful,":[116],"depending":[117],"congruence":[120,138],"class":[121],"mod":[124],"n":[125],"curves":[129],"resemble":[131],"double":[133],"helix":[134],"within":[135],"class.":[139],"also":[141],"consider":[142],"total":[144],"repeated":[147],"irreducible":[148],"summands":[149],"direct":[152],"sum":[153],"decomposition":[154],"space":[160],"fixed":[166],"dimension,":[167],"plot":[169],"its":[170],"histogram.":[171],"This":[172],"related":[174],"concept":[177],"(used":[178],"quantum":[180],"information":[181],"theory)":[182],"noiseless":[184],"subsystem.":[185],"identify":[187],"simple":[189],"conjectured":[193],"be":[195],"asymptotic":[197],"form":[198],"aforementioned":[201],"histogram,":[202],"verify":[204],"numerically":[205],"this":[207],"correct":[209],"n.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}