{"id":"https://openalex.org/W3000750619","doi":"https://doi.org/10.1080/00029890.2021.1856582","title":"On Arithmetic Progressions of Powers in Cyclotomic Polynomials","display_name":"On Arithmetic Progressions of Powers in Cyclotomic Polynomials","publication_year":2021,"publication_date":"2021-02-18","ids":{"openalex":"https://openalex.org/W3000750619","doi":"https://doi.org/10.1080/00029890.2021.1856582","mag":"3000750619"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2021.1856582","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2021.1856582","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"The American Mathematical Monthly","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/2001.08065","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070018996","display_name":"H\u00f9ng Vi\u1ec7t Chu","orcid":"https://orcid.org/0000-0002-9966-0038"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"H\u00f9ng Vi\u1ec7t Chu","raw_affiliation_strings":["Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61820","Department of Mathematics, University of Illinois at Urbana-Champaign , Urbana , IL 61820 hungchu2@illinois.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61820","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Mathematics, University of Illinois at Urbana-Champaign , Urbana , IL 61820 hungchu2@illinois.edu","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070018996"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02946593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"128","issue":"3","first_page":"268","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9930999875068665,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9905999898910522,"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/arithmetic","display_name":"Arithmetic","score":0.7210909724235535},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6993910074234009},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.4141600728034973},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3380466103553772},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32974112033843994}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7210909724235535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6993910074234009},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.4141600728034973},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3380466103553772},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32974112033843994}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00029890.2021.1856582","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2021.1856582","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2001.08065","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.08065","pdf_url":"https://arxiv.org/pdf/2001.08065","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:3000750619","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2001.08065","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.2001.08065","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.08065","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-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.08065","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.08065","pdf_url":"https://arxiv.org/pdf/2001.08065","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":0.8600000143051147,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000750619.pdf","grobid_xml":"https://content.openalex.org/works/W3000750619.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1990664192","https://openalex.org/W2042641733","https://openalex.org/W2066564346","https://openalex.org/W2093313826","https://openalex.org/W2313001132","https://openalex.org/W2325571892","https://openalex.org/W2333950682","https://openalex.org/W2962706819","https://openalex.org/W2964157376"],"related_works":["https://openalex.org/W1993694814","https://openalex.org/W2026541554","https://openalex.org/W2998003038","https://openalex.org/W2072409983","https://openalex.org/W2952338868","https://openalex.org/W2953273942","https://openalex.org/W1997500364","https://openalex.org/W2773611110","https://openalex.org/W2121933854","https://openalex.org/W2963417776","https://openalex.org/W3099143670","https://openalex.org/W2175270757","https://openalex.org/W2899984794","https://openalex.org/W3042914155","https://openalex.org/W3016165551","https://openalex.org/W2984220964","https://openalex.org/W2593477490","https://openalex.org/W3100417154","https://openalex.org/W2075267144"],"abstract_inverted_index":{"We":[0],"determine":[1],"necessary":[2],"conditions":[3,26],"for":[4,21],"when":[5,35],"powers":[6],"corresponding":[7],"to":[8,39],"positive/negative":[9],"coefficients":[10],"of":[11],"\u03a6n":[12],"are":[13,27],"in":[14],"arithmetic":[15],"progression.":[16],"When":[17],"n":[18,36],"=":[19,37],"pq":[20,38],"any":[22],"primes":[23],"q>p>2,":[24],"our":[25],"also":[28],"sufficient.":[29],"Finally,":[30],"we":[31],"generalize":[32],"the":[33,40],"result":[34],"so-called":[41],"inclusion-exclusion":[42],"polynomials":[43],"first":[44],"introduced":[45],"by":[46],"Bachman.":[47]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
