{"id":"https://openalex.org/W2963670058","doi":"https://doi.org/10.1080/10586458.2015.1107870","title":"Lehmer Pairs Revisited","display_name":"Lehmer Pairs Revisited","publication_year":2016,"publication_date":"2016-07-07","ids":{"openalex":"https://openalex.org/W2963670058","doi":"https://doi.org/10.1080/10586458.2015.1107870","mag":"2963670058"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2015.1107870","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2015.1107870","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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/A5080792963","display_name":"Jeffrey Stopple","orcid":"https://orcid.org/0000-0003-1857-5008"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeffrey Stopple","raw_affiliation_strings":["Mathematics Department, University of California, Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of California, Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080792963"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":1.0454,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.81610718,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"1","first_page":"45","last_page":"53"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9983000159263611,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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":0.7988883256912231},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.7303326725959778},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.503074586391449},{"id":"https://openalex.org/keywords/de-bruijn-sequence","display_name":"De Bruijn sequence","score":0.49639731645584106},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4629441499710083},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.4244394898414612},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4187588691711426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40513911843299866},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38920801877975464},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07299861311912537}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7988883256912231},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.7303326725959778},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.503074586391449},{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.49639731645584106},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4629441499710083},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.4244394898414612},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4187588691711426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40513911843299866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38920801877975464},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07299861311912537},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2015.1107870","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2015.1107870","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1224069186","https://openalex.org/W1980116773","https://openalex.org/W2008486284","https://openalex.org/W2039017895","https://openalex.org/W2080252578","https://openalex.org/W2092645710","https://openalex.org/W2093285600","https://openalex.org/W2106226212","https://openalex.org/W2112068204","https://openalex.org/W2175186690","https://openalex.org/W4239940795","https://openalex.org/W4254906725"],"related_works":["https://openalex.org/W2610184042","https://openalex.org/W2964407532","https://openalex.org/W4294651012","https://openalex.org/W1513480133","https://openalex.org/W2986559382","https://openalex.org/W2086661656","https://openalex.org/W3200545397","https://openalex.org/W4288019650","https://openalex.org/W2909634389","https://openalex.org/W3129435903"],"abstract_inverted_index":{"We":[0,92,152],"seek":[1],"to":[2,15,174],"understand":[3],"how":[4],"the":[5,20,25,28,37,57,62,81,88,101,104,175,181],"technical":[6],"definition":[7],"of":[8,19,27,30,55,71,103,106,130,146,150,157,159,178],"a":[9],"Lehmer":[10,78,95,119,122,169],"pair":[11],"can":[12],"be":[13],"related":[14],"more":[16],"analytic":[17],"properties":[18],"Riemann":[21,63,89],"zeta":[22],"function,":[23],"particularly":[24],"location":[26],"zeros":[29,148,158,177],"\u03b6\u2032(s).":[31,151],"Because":[32],"we":[33,86],"are":[34,121,172],"interested":[35],"in":[36,128,144,180],"connection":[38],"[Csordas":[39,43],"et":[40,44],"al.":[41,45],"94":[42],"94]":[46],"G.":[47],"Csordas,":[48],"W.":[49],"Smith,":[50],"R.":[51],"Varga.":[52],"\u201cLehmer":[53],"Pairs":[54],"Zeros,":[56],"de":[58,82],"Bruijn-Newman":[59],"Constant,":[60],"and":[61,80],"Hypothesis.\u201d":[64],"Constr.":[65],"Approx.":[66],"10":[67],"(1994),":[68],"107\u2013129.[Crossref],":[69],"[Web":[70],"Science":[72],"\u00ae]":[73],",":[74],"[Google":[75],"Scholar]]":[76],"between":[77],"pairs":[79,96,120,156],"Bruijn\u2013Newman":[83],"constant":[84],"\u039b,":[85],"assume":[87],"hypothesis":[90],"throughout.":[91],"define":[93],"strong":[94,118,168],"via":[97],"an":[98],"inequality":[99],"on":[100],"derivative":[102],"pre-Schwarzian":[105],"Riemann\u2019s":[107],"function":[108],"\u039e(t),":[109],"evaluated":[110],"at":[111],"consecutive":[112],"zeros:":[113],"Theorem":[114,124,138],"1":[115],"shows":[116],"that":[117],"pairs.":[123,170],"2":[125],"describes":[126],"P\u039e\u2032(\u03b3)":[127],"terms":[129,145],"\u03b6\u2032(\u03c1)":[131],"where":[132],"\u03c1":[133],"=":[134,164],"1/2":[135],"+":[136,142],"i\u03b3.":[137],"3":[139],"expresses":[140],"P\u039e\u2032(\u03b3+)":[141],"P\u039e\u2032(\u03b3\u2212)":[143],"nearby":[147],"\u03c1\u2032":[149],"examine":[153],"114,":[154],"661":[155],"\u03b6(s)":[160],"around":[161],"height":[162],"t":[163],"106,":[165],"finding":[166],"855":[167],"These":[171],"compared":[173],"corresponding":[176],"\u03b6\u2032(s)":[179],"same":[182],"range.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}