{"id":"https://openalex.org/W2034049250","doi":"https://doi.org/10.1090/s0025-5718-97-00801-6","title":"Computational experiences on the distances of polynomials to irreducible polynomials","display_name":"Computational experiences on the distances of polynomials to irreducible polynomials","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2034049250","doi":"https://doi.org/10.1090/s0025-5718-97-00801-6","mag":"2034049250"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-97-00801-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00801-6","pdf_url":"https://www.ams.org/mcom/1997-66-217/S0025-5718-97-00801-6/S0025-5718-97-00801-6.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1997-66-217/S0025-5718-97-00801-6/S0025-5718-97-00801-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081151822","display_name":"Attila B\u00e9rczes","orcid":null},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"A. B\u00e9rczes","raw_affiliation_strings":["Department of Mathematics and Informatics, Kossuth Lajos University, 4010 Debrecen, Pf. 12, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Kossuth Lajos University, 4010 Debrecen, Pf. 12, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035526712","display_name":"Lajos Hajdu","orcid":"https://orcid.org/0000-0003-1651-1238"},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"L. Hajdu","raw_affiliation_strings":["Department of Mathematics and Informatics, Kossuth Lajos University, 4010 Debrecen, Pf. 12, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Kossuth Lajos University, 4010 Debrecen, Pf. 12, Hungary","institution_ids":["https://openalex.org/I132735039"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I132735039"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.1336525,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"66","issue":"217","first_page":"391","last_page":"399"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.9987999796867371,"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/monic-polynomial","display_name":"Monic polynomial","score":0.9455358982086182},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8491097092628479},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5986208915710449},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5888436436653137},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5631492137908936},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.4537201523780823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36644694209098816},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.19631457328796387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11373069882392883},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.057174623012542725}],"concepts":[{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.9455358982086182},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8491097092628479},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5986208915710449},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5888436436653137},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5631492137908936},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.4537201523780823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36644694209098816},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.19631457328796387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11373069882392883},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.057174623012542725},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-97-00801-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00801-6","pdf_url":"https://www.ams.org/mcom/1997-66-217/S0025-5718-97-00801-6/S0025-5718-97-00801-6.pdf","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.107.9906","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.107.9906","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1997-66-217/S0025-5718-97-00801-6/S0025-5718-97-00801-6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.5020","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.5020","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/1997-66-217/S0025-5718-97-00801-6/S0025-5718-97-00801-6.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-97-00801-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00801-6","pdf_url":"https://www.ams.org/mcom/1997-66-217/S0025-5718-97-00801-6/S0025-5718-97-00801-6.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2034049250.pdf","grobid_xml":"https://content.openalex.org/works/W2034049250.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W855001296","https://openalex.org/W1569612250","https://openalex.org/W1848174884","https://openalex.org/W1968140699","https://openalex.org/W2014997928","https://openalex.org/W2020505858","https://openalex.org/W2056319099","https://openalex.org/W2064759901","https://openalex.org/W2076538178","https://openalex.org/W2090783201","https://openalex.org/W2504054210","https://openalex.org/W4234345682","https://openalex.org/W4235982382","https://openalex.org/W4237422229","https://openalex.org/W4240597556"],"related_works":["https://openalex.org/W4283012387","https://openalex.org/W1985839497","https://openalex.org/W4200010336","https://openalex.org/W2937328185","https://openalex.org/W2003536029","https://openalex.org/W3042751680","https://openalex.org/W2021016070","https://openalex.org/W2588251761","https://openalex.org/W1982147532","https://openalex.org/W2054200117"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,21],"deal":[4],"with":[5,43],"a":[6,37],"problem":[7],"of":[8,13,31,58],"Tur\u00e1n":[9],"concerning":[10],"the":[11,56],"\u2018distance\u2019":[12,57],"polynomials":[14],"to":[15],"irreducible":[16,51],"polynomials.":[17],"Using":[18],"computational":[19],"methods":[20],"prove":[22],"that":[23,48],"for":[24],"any":[25],"monic":[26,38],"polynomial":[27,39],"$P\\in$":[28],"${\\mathbb":[29],"{Z}}[x]$":[30,42],"degree":[32],"$\\leq":[33,63],"22$":[34],"there":[35],"exists":[36],"$Q\\in":[40],"{\\mathbb":[41],"deg($Q$)":[44],"=":[45],"deg($P$)":[46],"such":[47],"$Q$":[49,61],"is":[50,62],"over":[52],"$\\mathbb":[53],"{Q}$":[54],"and":[55,60],"$P$":[59],"4$.":[64]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}