{"id":"https://openalex.org/W2563886771","doi":null,"title":"Estimation of the Partition Number: After Hardy and Ramanujan","display_name":"Estimation of the Partition Number: After Hardy and Ramanujan","publication_year":2016,"publication_date":"2016-12-16","ids":{"openalex":"https://openalex.org/W2563886771","mag":"2563886771"},"language":"en","primary_location":{"id":"mag:2563886771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1612.05526v2","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1612.05526v2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100748682","display_name":"Wen-Wei Li","orcid":"https://orcid.org/0000-0002-0271-4491","observed_orcids":["https://orcid.org/0000-0002-0271-4491"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wen-Wei Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5100748682"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9409000277519226,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9409000277519226,"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":0.02160000056028366,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.014800000004470348,"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/partition-function","display_name":"partition function","score":0.8029999732971191},{"id":"https://openalex.org/keywords/parameter-fitting","display_name":"parameter fitting","score":0.6129999756813049},{"id":"https://openalex.org/keywords/least-squares-fitting","display_name":"least squares fitting","score":0.7170000076293945},{"id":"https://openalex.org/keywords/integer-partitions","display_name":"integer partitions","score":0.37599998712539673}],"concepts":[{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.9156769514083862},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7445159554481506},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.640821099281311},{"id":"https://openalex.org/C2776836400","wikidata":"https://www.wikidata.org/wiki/Q31087","display_name":"Calculator","level":2,"score":0.554684579372406},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5136103630065918},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4953056871891022},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.470842570066452},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46289342641830444},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.42948848009109497},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4104742407798767},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23986276984214783},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2352083921432495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17049044370651245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14767926931381226},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2563886771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1612.05526v2","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2563886771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1612.05526v2","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2874301969","https://openalex.org/W2368270937","https://openalex.org/W7081665138","https://openalex.org/W7108323075","https://openalex.org/W2152369819","https://openalex.org/W1978322039","https://openalex.org/W4287901025","https://openalex.org/W2016968046","https://openalex.org/W3011267844","https://openalex.org/W4396242445"],"abstract_inverted_index":{"Sometimes":[0],"we":[1],"need":[2],"the":[3,7,23,56,62,65,96,116,121,124,141],"approximate":[4,97],"value":[5,98],"of":[6,64,99,123,144],"partition":[8,24],"number":[9,25],"in":[10,37,48,52,55,139],"a":[11,105],"simple":[12],"and":[13,60,74],"efficient":[14],"way.":[15],"There":[16],"are":[17,29,90],"already":[18],"several":[19,80],"formulae":[20,84],"to":[21,119],"calculate":[22],"p(n).":[26],"But":[27],"they":[28],"either":[30],"inconvenient":[31],"for":[32,88],"most":[33],"people":[34],"(not":[35],"majored":[36],"math)":[38],"who":[39],"do":[40,43],"not":[41],"want":[42],"write":[44],"programs,":[45],"or":[46],"unsatisfying":[47],"accuracy.":[49],"By":[50],"bringing":[51],"two":[53,66,125],"parameters":[54,67,126],"Hardy-Ramanujan's":[57],"Asymptotic":[58],"formula":[59],"fitting":[61,142],"data":[63,122],"by":[68,104,127],"least":[69],"square":[70],"method,":[71],"iteration":[72],"method":[73,135],"some":[75,145],"other":[76,146],"special":[77],"designed":[78],"methods,":[79],"revised":[81],"elementary":[82,129],"estimation":[83,94],"with":[85],"high":[86],"accuracy":[87],"p(n)":[89,100],"obtained.":[91],"With":[92],"these":[93],"formulae,":[95],"can":[101],"be":[102,137],"calculated":[103],"pocket":[106],"calculator":[107],"without":[108],"programming":[109],"function.":[110],"The":[111],"main":[112],"difficulty":[113],"is":[114,131],"that":[115],"usual":[117],"methods":[118],"fit":[120],"an":[128],"function":[130],"defective":[132],"here.":[133],"These":[134],"could":[136],"used":[138],"finding":[140],"functions":[143],"complex":[147],"data.":[148]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-09-21T07:43:02.447757","created_date":"2017-01-06T00:00:00"}