{"id":"https://openalex.org/W2541102083","doi":"https://doi.org/10.1090/mcom/3275","title":"Computations of the Mertens function and improved bounds on the Mertens conjecture","display_name":"Computations of the Mertens function and improved bounds on the Mertens conjecture","publication_year":2017,"publication_date":"2017-04-05","ids":{"openalex":"https://openalex.org/W2541102083","doi":"https://doi.org/10.1090/mcom/3275","mag":"2541102083"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3275","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3275","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":"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/A5066364826","display_name":"Gregory B. Hurst","orcid":"https://orcid.org/0000-0002-7650-8009"},"institutions":[{"id":"https://openalex.org/I65760639","display_name":"Wolfram Research (United States)","ror":"https://ror.org/03k118f17","country_code":"US","type":"company","lineage":["https://openalex.org/I65760639"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Greg Hurst","raw_affiliation_strings":["Wolfram Research Inc., 100 Trade Center Drive, Champaign, Illinois 61820"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wolfram Research Inc., 100 Trade Center Drive, Champaign, Illinois 61820","institution_ids":["https://openalex.org/I65760639"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066364826"],"corresponding_institution_ids":["https://openalex.org/I65760639"],"apc_list":null,"apc_paid":null,"fwci":3.3023,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.91349398,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"87","issue":"310","first_page":"1013","last_page":"1028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9991000294685364,"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":0.9983000159263611,"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/mathematics","display_name":"Mathematics","score":0.8885070085525513},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.724993884563446},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4516085088253021},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3726358711719513},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34587275981903076},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11873242259025574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8885070085525513},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.724993884563446},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4516085088253021},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3726358711719513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34587275981903076},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11873242259025574}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3275","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3275","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1978196283","https://openalex.org/W1997459600","https://openalex.org/W1998944804","https://openalex.org/W2013585949","https://openalex.org/W2027537091","https://openalex.org/W2042581448","https://openalex.org/W2046089326","https://openalex.org/W2065409996","https://openalex.org/W2106226212","https://openalex.org/W2146844680","https://openalex.org/W2321449699","https://openalex.org/W2578557174","https://openalex.org/W4230326687","https://openalex.org/W4231244305"],"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":{"The":[0,39,106],"Mertens":[1,40],"function":[2],"is":[3,35],"defined":[4],"as":[5],"M":[6,44,75,92,135],"(":[7,16,30,45,76,93,136],"x":[8,14,46,49,58,61,77,80,94,97,137],")":[9,18,32,47,78,95,138],"=":[10,20],"\u2211":[11],"n":[12,17,31],"\u2264":[13],"\u03bc":[15,29],"M(x)":[19,139],"\\sum":[21],"_{n":[22],"\\leq":[23],"x}":[24],"\\mu":[25,33],"(n)":[26,34],",":[27,64],"where":[28],"the":[36],"M\u00f6bius":[37],"function.":[38],"conjecture":[41],"states":[42],"|":[43,50],"/":[48,79,96],">":[51,55,59,62,81,87,98,103],"1":[52,56,60,63],"|M(x)/\\sqrt":[53],"{x}|":[54],"for":[57],"which":[65],"was":[66],"proven":[67],"false":[68],"in":[69],"1985":[70],"by":[71],"showing":[72],"lim":[73,90],"inf":[74],"\u2212":[82,126],"1.009":[83],"\\liminf":[84],"M(x)/\\sqrt":[85,101],"{x}":[86,102],"-1.009":[88],"and":[89,117,122,129],"sup":[91],"1.06":[99,104],"\\limsup":[100],".":[105,132],"same":[107],"techniques":[108],"used":[109],"were":[110],"revisited":[111],"here":[112],"with":[113],"present":[114],"day":[115],"hardware":[116],"algorithms,":[118],"giving":[119],"improved":[120],"lower":[121],"upper":[123],"bounds":[124],"of":[125],"1.837625":[127],"-1.837625":[128],"1.826054":[130,131],"In":[133],"addition,":[134],"wa":[140]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
