{"id":"https://openalex.org/W2000630573","doi":"https://doi.org/10.1080/10586458.2000.10504411","title":"Integral Geometry and Real Zeros of Thue\u2013Morse Polynomials","display_name":"Integral Geometry and Real Zeros of Thue\u2013Morse Polynomials","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2000630573","doi":"https://doi.org/10.1080/10586458.2000.10504411","mag":"2000630573"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2000.10504411","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2000.10504411","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2000.10504411","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":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2000.10504411","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008443234","display_name":"Christophe Doche","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Doche","raw_affiliation_strings":["Laboratoire d'Algorithmique Arithmetique, Universite Bordeaux I , 351, cours de la Lib\u00e9ration, F-33405 Talence Cedex France E-mail: cdoche@math.u-bordeaux.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Algorithmique Arithmetique, Universite Bordeaux I , 351, cours de la Lib\u00e9ration, F-33405 Talence Cedex France E-mail: cdoche@math.u-bordeaux.fr","institution_ids":["https://openalex.org/I15057530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107278093","display_name":"Michel Mend\u00e8s France","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Michel Mend\u00e8s France","raw_affiliation_strings":["Laboratoire d'Algorithmique Arithmetique, Universite Bordeaux I , 351, cours de la Lib\u00e9ration, F-33405 Talence Cedex France E-mail: mmf@math.u-bordeaux.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Algorithmique Arithmetique, Universite Bordeaux I , 351, cours de la Lib\u00e9ration, F-33405 Talence Cedex France E-mail: mmf@math.u-bordeaux.fr","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210166017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5024,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60469881,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"3","first_page":"339","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":1.0,"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/T12351","display_name":"Geometry and complex manifolds","score":1.0,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9987999796867371,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9821000099182129,"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/mathematics","display_name":"Mathematics","score":0.9305955171585083},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6141167283058167},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.6135029792785645},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5667591094970703},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5563633441925049},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5344539880752563},{"id":"https://openalex.org/keywords/morse-code","display_name":"Morse code","score":0.5014009475708008},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.4862631559371948},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4593193531036377},{"id":"https://openalex.org/keywords/morse-theory","display_name":"Morse theory","score":0.45459938049316406},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3598670959472656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28297632932662964}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9305955171585083},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6141167283058167},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6135029792785645},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5667591094970703},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5563633441925049},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5344539880752563},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.5014009475708008},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.4862631559371948},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4593193531036377},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.45459938049316406},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3598670959472656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28297632932662964},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2000.10504411","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2000.10504411","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2000.10504411","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/1045604669","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1045604669","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.1015","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.1015","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.u-bordeaux.fr/~cdoche/documents/thuemorse.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1080/10586458.2000.10504411","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2000.10504411","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2000.10504411","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2000630573.pdf","grobid_xml":"https://content.openalex.org/works/W2000630573.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1481438721","https://openalex.org/W1883919315","https://openalex.org/W1991486559","https://openalex.org/W1996931690","https://openalex.org/W2000790726","https://openalex.org/W2031247779","https://openalex.org/W2050700592","https://openalex.org/W2077142118","https://openalex.org/W2109519791","https://openalex.org/W2330216979","https://openalex.org/W2493227548","https://openalex.org/W2585780081","https://openalex.org/W2593708767"],"related_works":["https://openalex.org/W1595332435","https://openalex.org/W2548670722","https://openalex.org/W3084339456","https://openalex.org/W1966769279","https://openalex.org/W1976948755","https://openalex.org/W2037435271","https://openalex.org/W2182193748","https://openalex.org/W2208124994","https://openalex.org/W1482643998","https://openalex.org/W1482357698"],"abstract_inverted_index":{"We":[0,100],"study":[1,82],"the":[2,35,70,83,88,105],"average":[3,36,55,84],"number":[4,37,89],"of":[5,8,38,41,50,90,93],"intersecting":[6],"points":[7],"a":[9,47,74],"given":[10,73],"curve":[11],"with":[12],"random":[13,42],"hyperplanes":[14],"in":[15],"an":[16],"n-dimensional":[17],"Euclidean":[18],"space.":[19],"As":[20],"noticed":[21],"by":[22],"A.":[23],"Edelman":[24],"and":[25,108],"E.":[26],"Kostlan,":[27],"this":[28],"problem":[29],"is":[30,87],"closely":[31],"linked":[32],"to":[33,69],"finding":[34],"real":[39,48,60,75,91],"zeros":[40,61,92],"polynomials.":[43],"They":[44],"showed":[45],"that":[46],"polynomial":[49],"degree":[51],"n":[52,57],"has":[53],"on":[54],"log":[56],"+":[58,98],"O(1)":[59],"(M.":[62],"Kac's":[63],"theorem).":[64],"This":[65],"result":[66],"leads":[67],"us":[68],"following":[71],"problem:":[72],"sequence":[76],"(\u03b1":[77],"k":[78,80],")":[79],"\u220aN,":[81],"where":[85],"\u03c1(fn)":[86],"fn(X)":[94],"=":[95],"\u03b10+\u03b11X+":[96],"\u2026":[97],"\u03b1nXn.":[99],"give":[101],"theoretical":[102],"results":[103],"for":[104,111],"Thue\u2014Morse":[106],"polynomials":[107],"numerical":[109],"evidence":[110],"other":[112],"polvnomials":[113]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}