{"id":"https://openalex.org/W1930637611","doi":"https://doi.org/10.1090/mcom/3011","title":"On Pellet\u2019s Theorem for a class of lacunary polynomials","display_name":"On Pellet\u2019s Theorem for a class of lacunary polynomials","publication_year":2015,"publication_date":"2015-07-06","ids":{"openalex":"https://openalex.org/W1930637611","doi":"https://doi.org/10.1090/mcom/3011","mag":"1930637611"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3011","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3011","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081358638","display_name":"A. Melman","orcid":"https://orcid.org/0000-0001-6761-665X"},"institutions":[{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Melman","raw_affiliation_strings":["Department of Applied Mathematics, School of Engineering, Santa Clara University, California 95053"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Engineering, Santa Clara University, California 95053","institution_ids":["https://openalex.org/I16269868"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081358638"],"corresponding_institution_ids":["https://openalex.org/I16269868"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05511425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"85","issue":"298","first_page":"707","last_page":"716"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9976000189781189,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9962999820709229,"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/lacunary-function","display_name":"Lacunary function","score":0.9409705400466919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8570462465286255},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6130553483963013},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5748241543769836},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.5252681970596313},{"id":"https://openalex.org/keywords/reciprocal-polynomial","display_name":"Reciprocal polynomial","score":0.421970009803772},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.4149324297904968},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40003639459609985},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3791116774082184},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3768501877784729},{"id":"https://openalex.org/keywords/alternating-polynomial","display_name":"Alternating polynomial","score":0.3618953824043274},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14365339279174805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.050049275159835815}],"concepts":[{"id":"https://openalex.org/C63356602","wikidata":"https://www.wikidata.org/wiki/Q1986013","display_name":"Lacunary function","level":2,"score":0.9409705400466919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8570462465286255},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6130553483963013},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5748241543769836},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.5252681970596313},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.421970009803772},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.4149324297904968},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40003639459609985},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3791116774082184},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3768501877784729},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.3618953824043274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14365339279174805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.050049275159835815},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3011","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3011","pdf_url":null,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1511572470","https://openalex.org/W1557452007","https://openalex.org/W1968780660","https://openalex.org/W1970606629","https://openalex.org/W2148775106","https://openalex.org/W2610857016","https://openalex.org/W2963062829"],"related_works":["https://openalex.org/W148891984","https://openalex.org/W1964170686","https://openalex.org/W2023818677","https://openalex.org/W2110869895","https://openalex.org/W1543706171","https://openalex.org/W2379712779","https://openalex.org/W2889570586","https://openalex.org/W103050704","https://openalex.org/W2391577669","https://openalex.org/W2047844713"],"abstract_inverted_index":{"An":[0],"important":[1],"tool":[2],"to":[3,10],"separate":[4],"zeros":[5],"of":[6,35],"a":[7,33,46,49],"polynomial":[8,47],"according":[9],"their":[11],"moduli":[12],"without":[13],"actually":[14],"computing":[15],"them":[16],"is":[17],"Pellet\u2019s":[18],"theorem,":[19],"which":[20],"unfortunately":[21],"places":[22],"severe":[23],"restrictions":[24],"on":[25],"the":[26],"polynomial\u2019s":[27],"coefficients.":[28],"We":[29],"show":[30],"that":[31],"for":[32],"class":[34],"lacunary":[36],"polynomials":[37],"much":[38],"better":[39],"results":[40],"can":[41],"be":[42],"obtained":[43],"by":[44],"rewriting":[45],"as":[48],"matrix":[50],"polynomial.":[51]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
