{"id":"https://openalex.org/W2891449816","doi":"https://doi.org/10.1090/mcom/3583","title":"The error term in the prime number theorem","display_name":"The error term in the prime number theorem","publication_year":2020,"publication_date":"2020-08-19","ids":{"openalex":"https://openalex.org/W2891449816","doi":"https://doi.org/10.1090/mcom/3583","mag":"2891449816"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3583","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3583","pdf_url":null,"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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1809.03134","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064602704","display_name":"David J. Platt","orcid":"https://orcid.org/0000-0003-1926-1465"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"David J. Platt","raw_affiliation_strings":["School of Mathematics, University of Bristol, Bristol, United Kingdom","University of Bristol"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Bristol, Bristol, United Kingdom","institution_ids":["https://openalex.org/I36234482"]},{"raw_affiliation_string":"University of Bristol","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109901763","display_name":"Tim Trudgian","orcid":null},"institutions":[{"id":"https://openalex.org/I188329596","display_name":"University of Canberra","ror":"https://ror.org/04s1nv328","country_code":"AU","type":"education","lineage":["https://openalex.org/I188329596"]},{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]},{"id":"https://openalex.org/I40053085","display_name":"Australian Defence Force Academy","ror":"https://ror.org/02j5s7g39","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571","https://openalex.org/I40053085","https://openalex.org/I4394709116"]},{"id":"https://openalex.org/I4394709116","display_name":"UNSW Canberra","ror":"https://ror.org/0125wpx05","country_code":null,"type":"education","lineage":["https://openalex.org/I31746571","https://openalex.org/I4394709116"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Timothy S. Trudgian","raw_affiliation_strings":["School of Science, The University of New South Wales Canberra, Australia","AUSTRALIAN DEFENCE FORCE ACADEMY"],"affiliations":[{"raw_affiliation_string":"School of Science, The University of New South Wales Canberra, Australia","institution_ids":["https://openalex.org/I188329596","https://openalex.org/I31746571","https://openalex.org/I4394709116"]},{"raw_affiliation_string":"AUSTRALIAN DEFENCE FORCE ACADEMY","institution_ids":["https://openalex.org/I40053085"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064602704"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":0.5016,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55704296,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"90","issue":"328","first_page":"871","last_page":"881"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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":1.0,"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":0.9994999766349792,"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/T12504","display_name":"Mathematics and Applications","score":0.9965999722480774,"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/ramanujans-sum","display_name":"Ramanujan's sum","score":0.817808210849762},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7765092849731445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7487096786499023},{"id":"https://openalex.org/keywords/prime-number-theorem","display_name":"Prime number theorem","score":0.6082854866981506},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.5620349645614624},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.561445415019989},{"id":"https://openalex.org/keywords/mean-value-theorem","display_name":"Mean value theorem (divided differences)","score":0.5572232604026794},{"id":"https://openalex.org/keywords/multiplicative-number-theory","display_name":"Multiplicative number theory","score":0.5007445812225342},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.442089319229126},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35060203075408936},{"id":"https://openalex.org/keywords/prime-factor","display_name":"Prime factor","score":0.31979626417160034},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3032320737838745},{"id":"https://openalex.org/keywords/picard\u2013lindel\u00f6f-theorem","display_name":"Picard\u2013Lindel\u00f6f theorem","score":0.1938493847846985},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.1759083867073059},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06074848771095276}],"concepts":[{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.817808210849762},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7765092849731445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7487096786499023},{"id":"https://openalex.org/C40758505","wikidata":"https://www.wikidata.org/wiki/Q386292","display_name":"Prime number theorem","level":3,"score":0.6082854866981506},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.5620349645614624},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.561445415019989},{"id":"https://openalex.org/C139588767","wikidata":"https://www.wikidata.org/wiki/Q17098096","display_name":"Mean value theorem (divided differences)","level":4,"score":0.5572232604026794},{"id":"https://openalex.org/C190565394","wikidata":"https://www.wikidata.org/wiki/Q6935001","display_name":"Multiplicative number theory","level":4,"score":0.5007445812225342},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.442089319229126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35060203075408936},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.31979626417160034},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3032320737838745},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.1938493847846985},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.1759083867073059},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06074848771095276},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/mcom/3583","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3583","pdf_url":null,"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:research-information.bris.ac.uk:openaire_cris_publications/5ebb9806-22ee-4e70-8b02-d8a6f499819a","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/5ebb9806-22ee-4e70-8b02-d8a6f499819a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Platt, D J & Trudgian, T 2020, 'The error term in the prime number theorem', Mathematics of Computation, vol. 90, no. 328, pp. 871.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1809.03134","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.03134","pdf_url":"https://arxiv.org/pdf/1809.03134","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null},{"id":"mag:2891449816","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1809.03134.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.1809.03134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1809.03134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1809.03134","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.03134","pdf_url":"https://arxiv.org/pdf/1809.03134","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5600000023841858,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1076911461","display_name":null,"funder_award_id":"FT160100094","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G4985331266","display_name":null,"funder_award_id":"DP160100932","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G694729825","display_name":null,"funder_award_id":"EP/K034383/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W146905023","https://openalex.org/W845927106","https://openalex.org/W1480319329","https://openalex.org/W1486331565","https://openalex.org/W1507390359","https://openalex.org/W1552861997","https://openalex.org/W1567653974","https://openalex.org/W1978559180","https://openalex.org/W2059140607","https://openalex.org/W2167794699","https://openalex.org/W2281218105","https://openalex.org/W2541924216","https://openalex.org/W2780529152","https://openalex.org/W2801998207","https://openalex.org/W2963709257","https://openalex.org/W2964018490","https://openalex.org/W2964108423","https://openalex.org/W2986262373","https://openalex.org/W3035691016","https://openalex.org/W3124685533"],"related_works":["https://openalex.org/W3053937274","https://openalex.org/W1502258963","https://openalex.org/W2952983018","https://openalex.org/W1978559180","https://openalex.org/W1993315702","https://openalex.org/W2219889327","https://openalex.org/W2474874264","https://openalex.org/W2963555902","https://openalex.org/W2525703531","https://openalex.org/W1595665965","https://openalex.org/W3099622082","https://openalex.org/W2802408352","https://openalex.org/W3005778431","https://openalex.org/W2317737351","https://openalex.org/W3195261090","https://openalex.org/W2155788403","https://openalex.org/W3042265560","https://openalex.org/W3002877956","https://openalex.org/W1981452459","https://openalex.org/W589795616"],"abstract_inverted_index":{"We":[0,27],"make":[1],"explicit":[2],"a":[3,9,31],"theorem":[4,15],"of":[5,11,21],"Pintz,":[6],"which":[7,23],"gives":[8],"version":[10],"the":[12],"prime":[13],"number":[14],"with":[16],"error":[17],"term":[18],"roughly":[19],"square-root":[20],"that":[22],"was":[24],"previously":[25],"known.":[26],"apply":[28],"this":[29],"to":[30],"long-standing":[32],"problem":[33],"concerning":[34],"an":[35],"inequality":[36],"studied":[37],"by":[38],"Ramanujan.":[39]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}