{"id":"https://openalex.org/W2030459789","doi":"https://doi.org/10.1145/1145768.1145815","title":"A quantitative P\u00f3lya's Theorem with corner zeros","display_name":"A quantitative P\u00f3lya's Theorem with corner zeros","publication_year":2006,"publication_date":"2006-07-09","ids":{"openalex":"https://openalex.org/W2030459789","doi":"https://doi.org/10.1145/1145768.1145815","mag":"2030459789"},"language":"en","primary_location":{"id":"doi:10.1145/1145768.1145815","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145815","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5007788926","display_name":"Victoria Powers","orcid":"https://orcid.org/0000-0003-0149-0825"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Victoria Powers","raw_affiliation_strings":["Emory University, Atlanta, GA","Emory university, Atlanta, GA"],"affiliations":[{"raw_affiliation_string":"Emory University, Atlanta, GA","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Emory university, Atlanta, GA","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069949548","display_name":"Bruce Reznick","orcid":"https://orcid.org/0000-0002-6946-9451"},"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":false,"raw_author_name":"Bruce Reznick","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, Urbana, IL","[University of Illinois at Urbana-Champaign,Urbana,IL]"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Urbana, IL","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"[University of Illinois at Urbana-Champaign,Urbana,IL]","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007788926"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":null,"apc_paid":null,"fwci":2.7151,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.88880578,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"285","last_page":"289"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9976000189781189,"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/T12504","display_name":"Mathematics and Applications","score":0.9958999752998352,"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/simplex","display_name":"Simplex","score":0.7276743054389954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6676180362701416},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5909634232521057},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49501150846481323},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4873388707637787},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45728108286857605},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.43790942430496216},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4218143820762634},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4166394770145416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23887202143669128}],"concepts":[{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.7276743054389954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6676180362701416},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5909634232521057},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49501150846481323},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4873388707637787},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45728108286857605},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.43790942430496216},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4218143820762634},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4166394770145416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23887202143669128},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1145768.1145815","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1145768.1145815","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2006 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.112.7403","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.7403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/~vicki/pub/polya2.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.118.4119","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.118.4119","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/~vicki/pub/polya2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.81.6173","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.81.6173","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~reznick/paper48.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1657726652","https://openalex.org/W1996541174","https://openalex.org/W1997612180","https://openalex.org/W2037009101","https://openalex.org/W2037321097","https://openalex.org/W2047577886","https://openalex.org/W2056515977","https://openalex.org/W2067009408","https://openalex.org/W2120146316","https://openalex.org/W2137508197","https://openalex.org/W2156173273","https://openalex.org/W2162356480","https://openalex.org/W2166822874"],"related_works":["https://openalex.org/W2063021680","https://openalex.org/W2467119940","https://openalex.org/W2357922472","https://openalex.org/W3194077685","https://openalex.org/W2384278689","https://openalex.org/W2563365141","https://openalex.org/W2152758797","https://openalex.org/W2386777115","https://openalex.org/W4295552001","https://openalex.org/W3118880678"],"abstract_inverted_index":{"P\u00f3lya's":[0,41,107],"Theorem":[1,42,108],"says":[2],"that":[3],"if":[4],"p":[5,37,63,96],"is":[6,14,22],"a":[7,30,57],"homogeneous":[8],"polynomial":[9],"in":[10,47],"n":[11],"variables":[12],"which":[13,112],"positive":[15,39],"on":[16,64,75,97],"the":[17,23,26,60,65,79,84,86,89,92,98,120,123],"standard":[18],"n-simplex,":[19],"and":[20,50,91],"F":[21],"sum":[24],"of":[25,62,81,88,95,122],"variables,":[27],"then":[28],"for":[29,53,59],"sufficiently":[31],"large":[32],"exponent":[33],"N,":[34,76],"FN":[35],"*":[36],"has":[38,43],"coefficients.":[40],"had":[44],"many":[45],"applications":[46],"both":[48],"pure":[49],"applied":[51],"mathematics;":[52],"example":[54],"it":[55],"provides":[56],"certificate":[58],"positivity":[61],"simplex.":[66,99,124],"The":[67],"authors":[68],"have":[69,116],"previously":[70],"given":[71],"an":[72],"explicit":[73],"bound":[74],"determined":[77],"by":[78],"data":[80],"p;":[82],"namely,":[83],"degree,":[85],"size":[87],"coefficients":[90],"minimum":[93],"value":[94],"In":[100],"this":[101,105],"paper,":[102],"we":[103],"extend":[104],"quantitative":[106],"to":[109,115],"non-negative":[110],"polynomials":[111],"are":[113],"allowed":[114],"simple":[117],"zeros":[118],"at":[119],"corners":[121]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
