{"id":"https://openalex.org/W2029466395","doi":"https://doi.org/10.1080/10586458.1999.10504628","title":"On Cyclotomic Polynomials with \u00b1 1 Coefficients","display_name":"On Cyclotomic Polynomials with \u00b1 1 Coefficients","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2029466395","doi":"https://doi.org/10.1080/10586458.1999.10504628","mag":"2029466395"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.1999.10504628","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1999.10504628","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/A5029261392","display_name":"Peter Borwein","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Peter Borwein","raw_affiliation_strings":["Department of Mathematics and Statistics , Simon Fraser University , Burnaby , B.C. , Canada , V5A 1S6 E-mail: pborwein@cecm.sfu.ca"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , Simon Fraser University , Burnaby , B.C. , Canada , V5A 1S6 E-mail: pborwein@cecm.sfu.ca","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102097726","display_name":"Kwok-Kwong Stephen Choi","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Kwok-Kwong Stephen Choi","raw_affiliation_strings":["Department of Mathematics , University of British Columbia , Vancouver , B.C. , Canada ; V6T 1Z2 and Department of Mathematics and Statistics , Simon Fraser University , Burnaby , B.C. , Canada , V5A 1S6 E-mail: choi@cecm.sfu.ca"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of British Columbia , Vancouver , B.C. , Canada ; V6T 1Z2 and Department of Mathematics and Statistics , Simon Fraser University , Burnaby , B.C. , Canada , V5A 1S6 E-mail: choi@cecm.sfu.ca","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029261392"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":null,"apc_paid":null,"fwci":1.4909,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.78733032,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"8","issue":"4","first_page":"399","last_page":"407"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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/T11191","display_name":"Mathematical functions and polynomials","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cyclotomic-polynomial","display_name":"Cyclotomic polynomial","score":0.9177467823028564},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9104650020599365},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.7480913996696472},{"id":"https://openalex.org/keywords/reciprocal-polynomial","display_name":"Reciprocal polynomial","score":0.6038540601730347},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5747719407081604},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5403523445129395},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5140508413314819},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4920205771923065},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.48321735858917236},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.45419907569885254},{"id":"https://openalex.org/keywords/minimal-polynomial","display_name":"Minimal polynomial (linear algebra)","score":0.4344552159309387},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4245874285697937},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.21102088689804077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09976819157600403}],"concepts":[{"id":"https://openalex.org/C76253118","wikidata":"https://www.wikidata.org/wiki/Q1051983","display_name":"Cyclotomic polynomial","level":3,"score":0.9177467823028564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9104650020599365},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.7480913996696472},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.6038540601730347},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5747719407081604},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5403523445129395},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5140508413314819},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4920205771923065},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.48321735858917236},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.45419907569885254},{"id":"https://openalex.org/C30597210","wikidata":"https://www.wikidata.org/wiki/Q1163608","display_name":"Minimal polynomial (linear algebra)","level":5,"score":0.4344552159309387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4245874285697937},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.21102088689804077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09976819157600403},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.1999.10504628","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1999.10504628","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.3332","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.3332","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hkumath.hku.hk/~choi/paper/cyclotomic.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1509536479","https://openalex.org/W1524383063","https://openalex.org/W1529024100","https://openalex.org/W2102479507","https://openalex.org/W3151140615","https://openalex.org/W4254660365"],"related_works":["https://openalex.org/W183994585","https://openalex.org/W2978931920","https://openalex.org/W2003536029","https://openalex.org/W2937328185","https://openalex.org/W1976456789","https://openalex.org/W2165697811","https://openalex.org/W2010641749","https://openalex.org/W2952097881","https://openalex.org/W2011142789","https://openalex.org/W70023776"],"abstract_inverted_index":{"We":[0,94],"characterize":[1,38],"all":[2,30,39],"cyclotomic":[3,20,40,61,92,139],"polynomials":[4,41,102],"of":[5,32,56,103,119,130,133],"even":[6,57],"degree":[7,58,105],"with":[8,26,42,53,106],"coefficients":[9,28,54],"restricted":[10],"to":[11,123],"the":[12,73,131],"set":[13],"{+1,":[14],"\u22121}.":[15],"In":[16],"this":[17,97,124],"context":[18],"a":[19,117,127],"polynomial":[21,25,51],"is":[22,47,60,111,126],"any":[23],"monic":[24],"integer":[27],"and":[29,63,72,80],"roots":[31],"modulus":[33],"1.":[34],"Inter":[35],"alia":[36],"we":[37],"odd":[43,104],"coefficients.":[44,108],"The":[45],"characterization":[46,98],"as":[48],"follows.":[49],"A":[50],"P(x)":[52],"\u00b11":[55,107],"N\u2013l":[59],"if":[62,65],"only":[64],"where":[66,81],"N":[67],"=":[68],"P1P1":[69],"\u2026":[70],"Pr":[71],"Pi":[74],"are":[75],"primes,":[76],"not":[77],"necessarily":[78],"distinct,":[79],"\u03d5p(x)":[82],":=":[83],"(xp":[84],"\u2013":[85,88],"1)/":[86],"(x":[87],"1)":[89],"isthe":[90],"p-th":[91],"polynomial.":[93],"conjecture":[95,110],"that":[96],"also":[99],"holds":[100],"for":[101],"This":[109],"based":[112],"on":[113,138],"substantial":[114],"computation":[115],"plus":[116],"number":[118],"special":[120],"cases.":[121],"Central":[122],"paper":[125],"careful":[128],"analysis":[129],"effect":[132],"Graeffe's":[134],"root":[135],"squaring":[136],"algorithm":[137],"polynomials.":[140]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
