{"id":"https://openalex.org/W1484095440","doi":"https://doi.org/10.1090/s0002-9947-04-03766-3","title":"A quadratic approximation to the Sendov radius near the unit circle","display_name":"A quadratic approximation to the Sendov radius near the unit circle","publication_year":2004,"publication_date":"2004-10-19","ids":{"openalex":"https://openalex.org/W1484095440","doi":"https://doi.org/10.1090/s0002-9947-04-03766-3","mag":"1484095440"},"language":"lv","primary_location":{"id":"doi:10.1090/s0002-9947-04-03766-3","doi":"https://doi.org/10.1090/s0002-9947-04-03766-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-04-03766-3","pdf_url":"https://www.ams.org/tran/2005-357-03/S0002-9947-04-03766-3/S0002-9947-04-03766-3.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/tran/2005-357-03/S0002-9947-04-03766-3/S0002-9947-04-03766-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Michael Miller","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I51485169","display_name":"Le Moyne College","ror":"https://ror.org/00q369629","country_code":"US","type":"education","lineage":["https://openalex.org/I51485169"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Miller","raw_affiliation_strings":["Department of Mathematics, Le Moyne College, Syracuse, New York 13214"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Le Moyne College, Syracuse, New York 13214","institution_ids":["https://openalex.org/I51485169"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I51485169"],"apc_list":null,"apc_paid":null,"fwci":0.4905,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.58258326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"357","issue":"3","first_page":"851","last_page":"873"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.5034000277519226,"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/T11822","display_name":"Analytic and geometric function theory","score":0.5034000277519226,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.38600000739097595,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.05590000003576279,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/complex-polynomials","display_name":"complex polynomials","score":0.7950000166893005},{"id":"https://openalex.org/keywords/polynomial-roots","display_name":"polynomial roots","score":0.6200000047683716},{"id":"https://openalex.org/keywords/unit-disk","display_name":"unit disk","score":0.6000000238418579},{"id":"https://openalex.org/keywords/second-order-approximation","display_name":"second-order approximation","score":0.8370000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9123076796531677},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.7563093900680542},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6629652380943298},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.6457510590553284},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5578137636184692},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.4298233985900879},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4144187867641449},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3950229585170746},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0002-9947-04-03766-3","doi":"https://doi.org/10.1090/s0002-9947-04-03766-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-04-03766-3","pdf_url":"https://www.ams.org/tran/2005-357-03/S0002-9947-04-03766-3/S0002-9947-04-03766-3.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0310004","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0310004","pdf_url":"https://arxiv.org/pdf/math/0310004","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.4406","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.4406","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0310004v1.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.math/0310004","doi":"https://doi.org/10.48550/arxiv.math/0310004","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0310004","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1090/s0002-9947-04-03766-3","doi":"https://doi.org/10.1090/s0002-9947-04-03766-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-04-03766-3","pdf_url":"https://www.ams.org/tran/2005-357-03/S0002-9947-04-03766-3/S0002-9947-04-03766-3.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1484095440.pdf","grobid_xml":"https://content.openalex.org/works/W1484095440.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W84519218","https://openalex.org/W1557452007","https://openalex.org/W1560124954","https://openalex.org/W1968118147","https://openalex.org/W1980545160","https://openalex.org/W2003286773","https://openalex.org/W2006381381","https://openalex.org/W2007044614","https://openalex.org/W2032597625","https://openalex.org/W2034969455","https://openalex.org/W2074433753","https://openalex.org/W2129428675","https://openalex.org/W3149857766"],"related_works":["https://openalex.org/W4415120791","https://openalex.org/W1557341032","https://openalex.org/W1551069853","https://openalex.org/W2012090423","https://openalex.org/W2320679898","https://openalex.org/W4321448590","https://openalex.org/W4386617190","https://openalex.org/W2607092220","https://openalex.org/W2006381381","https://openalex.org/W2804953499"],"abstract_inverted_index":{"Define":[0],"S":[1,86],"(":[2,73,87,116],"n":[3,18,72,88,115],",":[4,44,89],"\u03b2":[5,36,49,56,74,82,90,117],")":[6,8,75,91,101,118],"S(n,\\beta":[7,100],"to":[9,51],"be":[10,52],"the":[11,27,53,59,63,133],"set":[12],"of":[13,16,62,109],"complex":[14],"polynomials":[15],"degree":[17],"\u2265":[19],"2":[20,22],"n\\ge":[21],"with":[23],"all":[24],"roots":[25],"in":[26],"unit":[28,134],"disk":[29],"and":[30,58],"at":[31,35],"least":[32],"one":[33],"root":[34,61],"\\beta":[37,57],".":[38,68,103,124],"For":[39],"a":[40,107],"polynomial":[41],"P":[42,43,47,65,80,84,98],"define":[45,70],"|":[46,48,79,81],"|P|_\\beta":[50,96],"distance":[54],"between":[55],"closest":[60],"derivative":[64],"\u2032":[66],"P\u2019":[67],"Finally,":[69],"r":[71,114],"=":[76],"sup":[77],"{":[78],":":[83,97],"\u2208":[85],"}":[92],"r_n(\\beta":[93,121],")=\\sup":[94],"\\{":[95],"\\in":[99],"\\}":[102],"In":[104,125],"this":[105,126],"notation,":[106],"conjecture":[108,131],"Bl.":[110],"Sendov":[111],"claims":[112],"that":[113],"\u2264":[119],"1":[120,123,140],")\\le":[122],"paper":[127],"we":[128],"investigate":[129],"Sendov\u2019s":[130],"near":[132],"circle,":[135],"by":[136],"computing":[137],"constants":[138],"C":[139],"C_1":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}