{"id":"https://openalex.org/W1997795239","doi":"https://doi.org/10.1080/10586458.2007.10129001","title":"Equality of Polynomial and Field Discriminants","display_name":"Equality of Polynomial and Field Discriminants","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1997795239","doi":"https://doi.org/10.1080/10586458.2007.10129001","mag":"1997795239"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2007.10129001","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129001","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/A5074970891","display_name":"Avner Ash","orcid":"https://orcid.org/0009-0008-8100-8237"},"institutions":[{"id":"https://openalex.org/I103531236","display_name":"Boston College","ror":"https://ror.org/02n2fzt79","country_code":"US","type":"education","lineage":["https://openalex.org/I103531236"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Avner Ash","raw_affiliation_strings":["Boston College, Chestnut Hill, MA 02445"],"affiliations":[{"raw_affiliation_string":"Boston College, Chestnut Hill, MA 02445","institution_ids":["https://openalex.org/I103531236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016611466","display_name":"Jos Brakenhoff","orcid":null},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jos Brakenhoff","raw_affiliation_strings":["Universiteit Leiden, Leiden, the Netherlands","Universiteit Leiden Leiden The Netherlands"],"affiliations":[{"raw_affiliation_string":"Universiteit Leiden, Leiden, the Netherlands","institution_ids":["https://openalex.org/I121797337"]},{"raw_affiliation_string":"Universiteit Leiden Leiden The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028456553","display_name":"Theodore Zarrabi","orcid":null},"institutions":[{"id":"https://openalex.org/I103531236","display_name":"Boston College","ror":"https://ror.org/02n2fzt79","country_code":"US","type":"education","lineage":["https://openalex.org/I103531236"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Theodore Zarrabi","raw_affiliation_strings":["Boston College, Chestnut Hill, MA 02445"],"affiliations":[{"raw_affiliation_string":"Boston College, Chestnut Hill, MA 02445","institution_ids":["https://openalex.org/I103531236"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074970891"],"corresponding_institution_ids":["https://openalex.org/I103531236"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.08874561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"3","first_page":"367","last_page":"374"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9876999855041504,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9876999855041504,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9456999897956848,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9453999996185303,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9660552740097046},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.9352917075157166},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8697906732559204},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6983298659324646},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.6426777839660645},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.6031901836395264},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5778846144676208},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.48196980357170105},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.43940597772598267},{"id":"https://openalex.org/keywords/square-free-polynomial","display_name":"Square-free polynomial","score":0.42920157313346863},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4272994101047516},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.4116286039352417},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40756940841674805},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39816534519195557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13638648390769958},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09687644243240356},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08854752779006958},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0628075897693634}],"concepts":[{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.9660552740097046},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.9352917075157166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8697906732559204},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6983298659324646},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.6426777839660645},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.6031901836395264},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5778846144676208},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.48196980357170105},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.43940597772598267},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.42920157313346863},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4272994101047516},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4116286039352417},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40756940841674805},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39816534519195557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13638648390769958},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09687644243240356},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08854752779006958},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0628075897693634}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.2007.10129001","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129001","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:CULeuclid:euclid.em/1204928536","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1204928536","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7699999809265137,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2055837562","https://openalex.org/W3007836994","https://openalex.org/W3021045634"],"related_works":["https://openalex.org/W2917630846","https://openalex.org/W1985839497","https://openalex.org/W2937328185","https://openalex.org/W3207921890","https://openalex.org/W2049824936","https://openalex.org/W2952764322","https://openalex.org/W4320339927","https://openalex.org/W4245225834","https://openalex.org/W2165697811","https://openalex.org/W1976750632"],"abstract_inverted_index":{"We":[0,29],"give":[1],"a":[2,42],"conjecture":[3,43],"concerning":[4,44],"when":[5,45],"the":[6,15,18,38,46],"discriminant":[7,16,47],"of":[8,17,24,48],"an":[9,49],"irreducible":[10,50],"monic":[11,51],"integral":[12,52],"polynomial":[13,53],"equals":[14],"field":[19],"defined":[20],"by":[21,37],"adjoining":[22],"one":[23],"its":[25],"roots":[26],"to":[27],"\u211a.":[28],"discuss":[30],"computational":[31,58],"evidence":[32,59],"for":[33,60],"it.":[34,61],"An":[35],"appendix":[36],"second":[39],"author":[40],"gives":[41],"is":[54],"square-free":[55],"and":[56],"some":[57]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}