{"id":"https://openalex.org/W1991103553","doi":"https://doi.org/10.1080/10586458.2001.10504427","title":"Irrationality Measures of log 2 and \u03c0/\u221a3","display_name":"Irrationality Measures of log 2 and \u03c0/\u221a3","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1991103553","doi":"https://doi.org/10.1080/10586458.2001.10504427","mag":"1991103553"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2001.10504427","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504427","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/A5058275399","display_name":"Nicolas Brisebarre","orcid":"https://orcid.org/0000-0002-4220-2132"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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":true,"raw_author_name":"Nicolas Brisebarre","raw_affiliation_strings":["Laboratoire A2X, CNRS UPRESA 5465, Universit\u00e9 Bordeaux I , 351, Cours de la Liberation, F-33405 , Talence , France E-mail: brisebar@math.u-bordeaux.fr"],"affiliations":[{"raw_affiliation_string":"Laboratoire A2X, CNRS UPRESA 5465, Universit\u00e9 Bordeaux I , 351, Cours de la Liberation, F-33405 , Talence , France E-mail: brisebar@math.u-bordeaux.fr","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058275399"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I15057530"],"apc_list":null,"apc_paid":null,"fwci":1.8399,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.81601294,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"1","first_page":"35","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9930999875068665,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9930999875068665,"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/T11166","display_name":"Analytic Number Theory Research","score":0.991599977016449,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9836999773979187,"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":0.9258415699005127},{"id":"https://openalex.org/keywords/irrationality","display_name":"Irrationality","score":0.7537855505943298},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.6403653025627136},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6326075792312622},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46420344710350037},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.400835245847702},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14328858256340027},{"id":"https://openalex.org/keywords/rationality","display_name":"Rationality","score":0.06469318270683289},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.049812883138656616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9258415699005127},{"id":"https://openalex.org/C2777019708","wikidata":"https://www.wikidata.org/wiki/Q1412340","display_name":"Irrationality","level":3,"score":0.7537855505943298},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.6403653025627136},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6326075792312622},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46420344710350037},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.400835245847702},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14328858256340027},{"id":"https://openalex.org/C201717286","wikidata":"https://www.wikidata.org/wiki/Q938185","display_name":"Rationality","level":2,"score":0.06469318270683289},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.049812883138656616},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2001.10504427","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504427","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W360449572","https://openalex.org/W1462137042","https://openalex.org/W1687491367","https://openalex.org/W2003115626","https://openalex.org/W2039362637","https://openalex.org/W2106909610","https://openalex.org/W2121737852","https://openalex.org/W2130990342","https://openalex.org/W2146181406","https://openalex.org/W2282140813","https://openalex.org/W2313278888","https://openalex.org/W4238754468"],"related_works":["https://openalex.org/W2339240151","https://openalex.org/W2026699385","https://openalex.org/W2379715095","https://openalex.org/W2917740599","https://openalex.org/W2928364590","https://openalex.org/W2393751025","https://openalex.org/W2041851878","https://openalex.org/W4250299898","https://openalex.org/W4224102236","https://openalex.org/W2736737644"],"abstract_inverted_index":{"Using":[0],"a":[1],"class":[2],"of":[3,13],"polynomials":[4],"that":[5],"generalizes":[6],"Legendre":[7],"polynomials,":[8],"we":[9],"unify":[10],"previous":[11],"works":[12],"E.":[14],"A.":[15,17],"Rukhadze,":[16],"K.":[18],"Dubitskas,":[19],"M.":[20],"Hata,":[21],"D.":[22],"V.":[23,26],"and":[24,33],"G.":[25],"Chudnovsky":[27],"about":[28],"irrationality":[29],"measuresof":[30],"log":[31],"2":[32],"\u03c0/\u221a3.":[34]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}