{"id":"https://openalex.org/W4405592065","doi":"https://doi.org/10.1017/s0305004124000306","title":"On a Mertens-type conjecture for number fields","display_name":"On a Mertens-type conjecture for number fields","publication_year":2024,"publication_date":"2024-11-01","ids":{"openalex":"https://openalex.org/W4405592065","doi":"https://doi.org/10.1017/s0305004124000306"},"language":"en","primary_location":{"id":"doi:10.1017/s0305004124000306","doi":"https://doi.org/10.1017/s0305004124000306","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0305004124000306","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B01C7628DF4D57CAE8410901FD6A9321/S0305004124000306a.pdf/div-class-title-on-a-mertens-type-conjecture-for-number-fields-div.pdf","source":{"id":"https://openalex.org/S4210239678","display_name":"Mathematical Proceedings of the Cambridge Philosophical Society","issn_l":"0305-0041","issn":["0305-0041","1469-8064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Proceedings of the Cambridge Philosophical Society","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B01C7628DF4D57CAE8410901FD6A9321/S0305004124000306a.pdf/div-class-title-on-a-mertens-type-conjecture-for-number-fields-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027566932","display_name":"Daniel J. Hu","orcid":"https://orcid.org/0000-0002-9942-7463","observed_orcids":["https://orcid.org/0000-0002-9942-7463","https://orcid.org/0009-0003-5451-8825"]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DANIEL HU","raw_affiliation_strings":["Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000, U.S.A. e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000, U.S.A. e-mail:","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057651589","display_name":"Ikuya Kaneko","orcid":"https://orcid.org/0000-0003-4518-1805","observed_orcids":["https://orcid.org/0000-0003-4518-1805"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"IKUYA KANEKO","raw_affiliation_strings":["The Division of Physics, Mathematics and Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, U.S.A. e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Division of Physics, Mathematics and Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, U.S.A. e-mail:","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073832188","display_name":"Spencer Martin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"SPENCER MARTIN","raw_affiliation_strings":["Department of Mathematics, University of Virginia, 141 Cabell Drive, Kerchof Hall, Charlottesville, VA 22904, U.S.A. e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Virginia, 141 Cabell Drive, Kerchof Hall, Charlottesville, VA 22904, U.S.A. e-mail:","institution_ids":["https://openalex.org/I51556381"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058866852","display_name":"Carl Schildkraut","orcid":"https://orcid.org/0009-0005-2574-0309","observed_orcids":["https://orcid.org/0009-0005-2574-0309"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"CARL SCHILDKRAUT","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, U.S.A. e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, U.S.A. e-mail:","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3450,"currency":"USD","value_usd":3450},"apc_paid":{"value":3450,"currency":"USD","value_usd":3450},"fwci":1.1179,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78855811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"177","issue":"3","first_page":"481","last_page":"523"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"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":0.0,"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/mertens-conjecture","display_name":"Mertens conjecture","score":0.9909999966621399},{"id":"https://openalex.org/keywords/number-fields","display_name":"number fields","score":0.9599999785423279},{"id":"https://openalex.org/keywords/mertens-function","display_name":"Mertens function","score":0.9760000109672546},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6748580932617188},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6535435914993286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5846281051635742},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3457271456718445},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34549033641815186},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06701314449310303},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0305004124000306","doi":"https://doi.org/10.1017/s0305004124000306","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0305004124000306","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B01C7628DF4D57CAE8410901FD6A9321/S0305004124000306a.pdf/div-class-title-on-a-mertens-type-conjecture-for-number-fields-div.pdf","source":{"id":"https://openalex.org/S4210239678","display_name":"Mathematical Proceedings of the Cambridge Philosophical Society","issn_l":"0305-0041","issn":["0305-0041","1469-8064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Proceedings of the Cambridge Philosophical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2109.06665","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.06665","pdf_url":"https://arxiv.org/pdf/2109.06665","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2109.06665","doi":"https://doi.org/10.48550/arxiv.2109.06665","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2109.06665","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1017/s0305004124000306","doi":"https://doi.org/10.1017/s0305004124000306","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0305004124000306","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B01C7628DF4D57CAE8410901FD6A9321/S0305004124000306a.pdf/div-class-title-on-a-mertens-type-conjecture-for-number-fields-div.pdf","source":{"id":"https://openalex.org/S4210239678","display_name":"Mathematical Proceedings of the Cambridge Philosophical Society","issn_l":"0305-0041","issn":["0305-0041","1469-8064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Proceedings of the Cambridge Philosophical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1203176449","display_name":null,"funder_award_id":"DMS 2002265","funder_id":"https://openalex.org/F4320327239","funder_display_name":"Templeton World Charity Foundation"},{"id":"https://openalex.org/G1366284332","display_name":null,"funder_award_id":"205118","funder_id":"https://openalex.org/F4320327239","funder_display_name":"Templeton World Charity Foundation"},{"id":"https://openalex.org/G218320337","display_name":null,"funder_award_id":"2002265","funder_id":"https://openalex.org/F4320310536","funder_display_name":"University of Virginia"},{"id":"https://openalex.org/G2184541125","display_name":null,"funder_award_id":"H98230-21-1-0059","funder_id":"https://openalex.org/F4320310536","funder_display_name":"University of Virginia"},{"id":"https://openalex.org/G2236695604","display_name":null,"funder_award_id":"DMS-2002265","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G2883382842","display_name":null,"funder_award_id":"2002265","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G3799111684","display_name":null,"funder_award_id":"205118","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4574309909","display_name":null,"funder_award_id":"2002265","funder_id":"https://openalex.org/F4320327239","funder_display_name":"Templeton World Charity Foundation"},{"id":"https://openalex.org/G4584290605","display_name":null,"funder_award_id":"H98230-21-1-0059","funder_id":"https://openalex.org/F4320327239","funder_display_name":"Templeton World Charity Foundation"},{"id":"https://openalex.org/G514166697","display_name":null,"funder_award_id":"205118","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G5310292134","display_name":null,"funder_award_id":"DMS-2002265","funder_id":"https://openalex.org/F4320310536","funder_display_name":"University of Virginia"},{"id":"https://openalex.org/G6325276776","display_name":null,"funder_award_id":"H98230-21-1-0059","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G638771317","display_name":null,"funder_award_id":"205118","funder_id":"https://openalex.org/F4320310536","funder_display_name":"University of Virginia"},{"id":"https://openalex.org/G6976582318","display_name":null,"funder_award_id":"DMS 205118","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G7745157626","display_name":null,"funder_award_id":"H98230-21-1-0059","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7845798442","display_name":null,"funder_award_id":"H98230","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G8053706774","display_name":null,"funder_award_id":"DMS 205118","funder_id":"https://openalex.org/F4320327239","funder_display_name":"Templeton World Charity Foundation"},{"id":"https://openalex.org/G8607994857","display_name":null,"funder_award_id":"DMS 205118","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8844109355","display_name":null,"funder_award_id":"DMS 205118","funder_id":"https://openalex.org/F4320310536","funder_display_name":"University of Virginia"},{"id":"https://openalex.org/G8929892664","display_name":"REU Site: Algebra and Number Theory at Emory University","funder_award_id":"2002265","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310536","display_name":"University of Virginia","ror":"https://ror.org/0153tk833"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320327239","display_name":"Templeton World Charity Foundation","ror":"https://ror.org/00x0z1472"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405592065.pdf","grobid_xml":"https://content.openalex.org/works/W4405592065.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W5542750","https://openalex.org/W5546779","https://openalex.org/W1566059526","https://openalex.org/W1637187037","https://openalex.org/W1944087348","https://openalex.org/W1976923416","https://openalex.org/W1978196283","https://openalex.org/W2010510777","https://openalex.org/W2041010262","https://openalex.org/W2044518158","https://openalex.org/W2054973121","https://openalex.org/W2061390205","https://openalex.org/W2069107165","https://openalex.org/W2072814072","https://openalex.org/W2090804474","https://openalex.org/W2095393613","https://openalex.org/W2101737148","https://openalex.org/W2133478167","https://openalex.org/W2146844680","https://openalex.org/W2158180956","https://openalex.org/W2158516334","https://openalex.org/W2170585976","https://openalex.org/W2321449699","https://openalex.org/W2480467406","https://openalex.org/W2541102083","https://openalex.org/W2578557174","https://openalex.org/W2983594669","https://openalex.org/W3104206352","https://openalex.org/W4214884342","https://openalex.org/W4245500462","https://openalex.org/W4247713505"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"We":[1,26],"introduce":[2],"a":[3,31],"number":[4,20,57],"field":[5],"analogue":[6],"of":[7,22,30,43,49,54,61],"the":[8,28,36,50],"Mertens":[9,38,52],"conjecture":[10],"and":[11],"demonstrate":[12],"its":[13],"falsity":[14],"for":[15,35],"all":[16],"but":[17],"finitely":[18],"many":[19],"fields":[21,58],"any":[23],"given":[24],"degree.":[25],"establish":[27],"existence":[29],"logarithmic":[32],"limiting":[33],"distribution":[34],"analogous":[37],"function,":[39],"expanding":[40],"upon":[41],"work":[42],"Ng.":[44],"Finally,":[45],"we":[46],"explore":[47],"properties":[48],"generalised":[51],"function":[53],"certain":[55],"dicyclic":[56],"as":[59],"consequences":[60],"Artin":[62],"factorisation.":[63]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}