{"id":"https://openalex.org/W1525092514","doi":"https://doi.org/10.1090/mcom/2999","title":"Finite differences of the logarithm of the partition function","display_name":"Finite differences of the logarithm of the partition function","publication_year":2015,"publication_date":"2015-07-22","ids":{"openalex":"https://openalex.org/W1525092514","doi":"https://doi.org/10.1090/mcom/2999","mag":"1525092514"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/2999","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/2999","pdf_url":"https://www.ams.org/mcom/2016-85-298/S0025-5718-2015-02999-8/S0025-5718-2015-02999-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2016-85-298/S0025-5718-2015-02999-8/S0025-5718-2015-02999-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074795333","display_name":"William Y. C. Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"William Chen","raw_affiliation_strings":["Center for Applied Mathematics, Tianjin University, Tianjin 300072, People\u00e2\u0080\u0099s Republic of China","Center for Applied Mathematics , Tianjin University , Tianjin 300072 , People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics, Tianjin University, Tianjin 300072, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Center for Applied Mathematics , Tianjin University , Tianjin 300072 , People's Republic of China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080703892","display_name":"Xingwei Wang","orcid":"https://orcid.org/0000-0002-9579-3837"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Larry Wang","raw_affiliation_strings":["Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u00e2\u0080\u0099s Republic of China","Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u2019s Republic of China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003350193","display_name":"Gary Y. B. Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gary Xie","raw_affiliation_strings":["Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u00e2\u0080\u0099s Republic of China","Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 30071, People\u2019s Republic of China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02857695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"85","issue":"298","first_page":"825","last_page":"847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9993000030517578,"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":0.9955999851226807,"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/combinatorics","display_name":"Combinatorics","score":0.7616205215454102},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7490881085395813},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.6349025964736938},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6324517726898193},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6049622297286987},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5803251266479492},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41078490018844604},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3237146735191345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14194855093955994},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06974193453788757}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7616205215454102},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7490881085395813},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.6349025964736938},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6324517726898193},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6049622297286987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5803251266479492},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41078490018844604},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3237146735191345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14194855093955994},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06974193453788757}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/2999","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/2999","pdf_url":"https://www.ams.org/mcom/2016-85-298/S0025-5718-2015-02999-8/S0025-5718-2015-02999-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1407.0177","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1407.0177","pdf_url":"https://arxiv.org/pdf/1407.0177","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,"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":"mag:1525092514","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1407.0177","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,"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},{"id":"doi:10.48550/arxiv.1407.0177","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1407.0177","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1090/mcom/2999","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/2999","pdf_url":"https://www.ams.org/mcom/2016-85-298/S0025-5718-2015-02999-8/S0025-5718-2015-02999-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2717198908","display_name":null,"funder_award_id":"973 Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1525092514.pdf","grobid_xml":"https://content.openalex.org/works/W1525092514.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2004035056","https://openalex.org/W6631343838","https://openalex.org/W6636662623"],"related_works":["https://openalex.org/W2964312531","https://openalex.org/W2737487492","https://openalex.org/W2235738670","https://openalex.org/W2725425987","https://openalex.org/W1888894765","https://openalex.org/W2950286990","https://openalex.org/W2951780910","https://openalex.org/W2416516157","https://openalex.org/W2895871368","https://openalex.org/W2889946104","https://openalex.org/W3154634303","https://openalex.org/W2086285540","https://openalex.org/W2100154915","https://openalex.org/W3112432612","https://openalex.org/W3008440773","https://openalex.org/W2962707174","https://openalex.org/W2951884958","https://openalex.org/W2958160124","https://openalex.org/W3008977270","https://openalex.org/W1979567118"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,32,140,169,308,347],"content-type=\"math/mathml\">":[2,33,141,170,309,348],"<mml:math":[3,34,142,171,310,349],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,35,143,172,311,350],"alttext=\"p":[5],"left-parenthesis":[6,38,45,49,61,66,175,182,186,206,211,358],"n":[7,39,46,55,62,67,176,183,195,207,212,359],"right-parenthesis\">":[8,362],"<mml:semantics>":[9,72,147,217,315],"<mml:mrow>":[10,73,75,87,96,108,116,148,218,220,232,241,249,271,279,316],"<mml:mi>p</mml:mi>":[11,76,88,109,117,221,233,272,280],"<mml:mo":[12,15,77,84,89,92,110,113,118,123,222,229,234,237,273,276,281,286],"stretchy=\"false\">(</mml:mo>":[13,78,90,111,119,223,235,274,282],"<mml:mi>n</mml:mi>":[14,79,91,102,112,120,149,224,236,254,275,283,317],"stretchy=\"false\">)</mml:mo>":[16,85,93,114,124,230,238,277,287],"</mml:mrow>":[17,86,94,105,115,125,127,154,231,239,261,263,265,268,278,288,290,322],"<mml:annotation":[18,128,155,291,323],"encoding=\"application/x-tex\">p(n)</mml:annotation>":[19],"</mml:semantics>":[20,136,158,303,326],"</mml:math>":[21,137,159,304,327],"</inline-formula>":[22,138,160,305,328],"denote":[23],"the":[24,335],"partition":[25],"function.":[26],"DeSalvo":[27],"and":[28,339],"Pak":[29,340],"proved":[30],"that":[31,165],"alttext=\"StartFraction":[36,173],"p":[37,44,60,65,174,181,205,210,357],"minus":[40,177,360],"1":[41,50,53,69,178,187,214,361],"right-parenthesis":[42,47,57,63,70,179,184,202,208,215],"Over":[43,54,64,180,191,209],"EndFraction":[48,56,185,201],"plus":[51,68,188,213],"StartFraction":[52,59,189,204],"greater-than":[58,203],"EndFraction\">":[71,216],"<mml:mfrac>":[74,100,107,219,245,270],"<mml:mo>":[80,150,225,318],"\u2212":[81,226],"</mml:mo>":[82,152,227,320],"<mml:mn>1</mml:mn>":[83,98,101,122,228,243,285],"</mml:mfrac>":[95,103,126,240,266,289],"<mml:mo>(</mml:mo>":[97,242],"<mml:mo>+</mml:mo>":[99,121,244,284],"<mml:mo>)</mml:mo>":[104,267],"<mml:mo>&gt;</mml:mo>":[106,269],"encoding=\"application/x-tex\">\\frac":[129,292],"{p(n-1)}{p(n)}\\left":[130,293],"(1+\\frac":[131],"{1}{n}\\right":[132],")&gt;":[133],"\\frac":[134,301],"{p(n)}{p(n+1)}</mml:annotation>":[135,302],"for":[139,307,346],"alttext=\"n":[144,312],"greater-than-or-equal-to":[145,313],"2\">":[146],"\u2265":[151,319],"<mml:mn>2</mml:mn>":[153,262],"encoding=\"application/x-tex\">n\\geq":[156,324],"2</mml:annotation>":[157],".":[161,329],"Moreover,":[162],"they":[163],"conjectured":[164],"a":[166],"sharper":[167],"inequality":[168],"pi":[190],"StartRoot":[192],"24":[193],"EndRoot":[194],"Superscript":[196],"3":[197],"slash":[198],"2":[199],"Baseline":[200],"<mml:mi>":[246],"\u03c0":[247],"</mml:mi>":[248],"<mml:msqrt>":[250],"<mml:mn>24</mml:mn>":[251],"</mml:msqrt>":[252],"<mml:msup>":[253],"<mml:mrow":[255,258],"class=\"MJX-TeXAtom-ORD\">":[256,259],"<mml:mn>3</mml:mn>":[257],"<mml:mo>/</mml:mo>":[260],"</mml:msup>":[264],"(":[294],"1+\\frac":[295],"{\\pi":[296],"}{\\sqrt":[297],"{24}n^{3/2}}\\right":[298],")":[299],"&gt;":[300],"holds":[306],"45\">":[314],"<mml:mn>45</mml:mn>":[321],"45</mml:annotation>":[325],"In":[330],"this":[331],"paper,":[332],"we":[333],"prove":[334],"conjecture":[336],"of":[337],"Desalvo":[338],"by":[341],"giving":[342],"an":[343],"upper":[344,353],"bound":[345],"alttext=\"minus":[351],"normal":[352],"Delta":[354],"squared":[355],"log":[356]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}