{"id":"https://openalex.org/W3112933313","doi":"https://doi.org/10.4007/annals.2026.204.2.1","title":"Mahler's method in several variables and finite automata","display_name":"Mahler's method in several variables and finite automata","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W3112933313","doi":"https://doi.org/10.4007/annals.2026.204.2.1","mag":"3112933313"},"language":"en","primary_location":{"id":"doi:10.4007/annals.2026.204.2.1","doi":"https://doi.org/10.4007/annals.2026.204.2.1","is_oa":false,"landing_page_url":"https://doi.org/10.4007/annals.2026.204.2.1","pdf_url":null,"source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2012.08283","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000184641","display_name":"Boris Adamczewski","orcid":"https://orcid.org/0000-0002-5893-8590","observed_orcids":["https://orcid.org/0000-0002-5893-8590"]},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I4387154239","display_name":"Centre International de Rencontres Math\u00e9matiques","ror":"https://ror.org/04e3d6y73","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4387153264","https://openalex.org/I4387154239"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Boris Adamczewski","raw_affiliation_strings":["Universit\u00e9 Lyon 1, CNRS, Institut Camille Jordan, ICJ UMR 5208, 69622 Villeurbanne, France and CNRS, Centre International de Recontres Math\u00e9matiques CIRM\nUAR 822, 13009 Marseille, France"],"raw_orcid":"https://orcid.org/0000-0002-5893-8590","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Lyon 1, CNRS, Institut Camille Jordan, ICJ UMR 5208, 69622 Villeurbanne, France and CNRS, Centre International de Recontres Math\u00e9matiques CIRM\nUAR 822, 13009 Marseille, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210104796","https://openalex.org/I4387154239"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024456603","display_name":"Colin Faverjon","orcid":"https://orcid.org/0009-0008-7174-3780","observed_orcids":["https://orcid.org/0009-0008-7174-3780"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210163673","display_name":"Laboratoire Ami\u00e9nois de Math\u00e9matique Fondamentale et Appliqu\u00e9e","ror":"https://ror.org/04smxbm79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210163673","https://openalex.org/I4647051"]},{"id":"https://openalex.org/I4647051","display_name":"Universit\u00e9 de Picardie Jules Verne","ror":"https://ror.org/01gyxrk03","country_code":"FR","type":"education","lineage":["https://openalex.org/I4647051"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Colin Faverjon","raw_affiliation_strings":["Universit\u00e9 Picardie Jules Verne, CNRS, LAMFA UMR 7352, 80039 Amiens, France"],"raw_orcid":"https://orcid.org/0009-0008-7174-3780","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Picardie Jules Verne, CNRS, LAMFA UMR 7352, 80039 Amiens, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210163673","https://openalex.org/I4647051"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9853,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.91577356,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":96},"biblio":{"volume":"204","issue":"2","first_page":"455","last_page":"533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.23229999840259552,"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/T11567","display_name":"semigroups and automata theory","score":0.23229999840259552,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.15880000591278076,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.14059999585151672,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/multiple-variables","display_name":"several variables","score":0.7940000295639038},{"id":"https://openalex.org/keywords/finite-state-machines","display_name":"finite automata","score":0.7929999828338623},{"id":"https://openalex.org/keywords/transcendence","display_name":"transcendence","score":0.7480000257492065},{"id":"https://openalex.org/keywords/algebraic-independence","display_name":"algebraic independence","score":0.9980000257492065},{"id":"https://openalex.org/keywords/automatic-sequences","display_name":"automatic sequences","score":0.5759999752044678},{"id":"https://openalex.org/keywords/cobham-s-theorem","display_name":"Cobham's theorem","score":0.9829999804496765}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.765887975692749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.614673912525177},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5702123641967773},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5136191248893738},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5031904578208923},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4674447774887085},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4547041356563568},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4311264157295227},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3211025595664978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25296807289123535},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.4007/annals.2026.204.2.1","doi":"https://doi.org/10.4007/annals.2026.204.2.1","is_oa":false,"landing_page_url":"https://doi.org/10.4007/annals.2026.204.2.1","pdf_url":null,"source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.08283","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.08283","pdf_url":"https://arxiv.org/pdf/2012.08283","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:HAL:hal-04763287v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-04763287/document","pdf_url":"https://hal.science/hal-04763287v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Annals of Mathematics, 2024, 204 (2), pp.455-533. &#x27E8;10.4007/annals.2026.204.2.1&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:3112933313","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2012.08283.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-04763287v2","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-04763287","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Annals of Mathematics, 2024, 204 (2), pp.455-533. &#x27E8;10.4007/annals.2026.204.2.1&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-05797618v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05797618","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Annals of Mathematics, 2026, 204 (2), pp.455-533. &#x27E8;10.4007/annals.2026.204.2.1&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2012.08283","doi":"https://doi.org/10.48550/arxiv.2012.08283","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2012.08283","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2012.08283","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.08283","pdf_url":"https://arxiv.org/pdf/2012.08283","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7739362011","display_name":"Automata in Number Theory","funder_award_id":"648132","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3112933313.pdf","grobid_xml":"https://content.openalex.org/works/W3112933313.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W43370847","https://openalex.org/W71805842","https://openalex.org/W80650342","https://openalex.org/W1483208600","https://openalex.org/W1486574671","https://openalex.org/W1489341787","https://openalex.org/W1590003630","https://openalex.org/W1615677161","https://openalex.org/W1967795793","https://openalex.org/W1971420167","https://openalex.org/W1976857385","https://openalex.org/W1987467476","https://openalex.org/W1999989993","https://openalex.org/W2004611557","https://openalex.org/W2025977119","https://openalex.org/W2029520222","https://openalex.org/W2030999998","https://openalex.org/W2031429268","https://openalex.org/W2059735611","https://openalex.org/W2088188364","https://openalex.org/W2120367467","https://openalex.org/W2122224295","https://openalex.org/W2128110882","https://openalex.org/W2128565143","https://openalex.org/W2131705730","https://openalex.org/W2148878902","https://openalex.org/W2150240096","https://openalex.org/W2204507128","https://openalex.org/W2237130070","https://openalex.org/W2330062860","https://openalex.org/W2390980631","https://openalex.org/W2490020473","https://openalex.org/W2538477359","https://openalex.org/W2578474161","https://openalex.org/W2596242161","https://openalex.org/W2890527859","https://openalex.org/W2890985056","https://openalex.org/W2962754787","https://openalex.org/W2963099546","https://openalex.org/W2963417818","https://openalex.org/W2963685888","https://openalex.org/W2977830815","https://openalex.org/W3010514372","https://openalex.org/W3093106422","https://openalex.org/W3102742192","https://openalex.org/W4221162319"],"related_works":["https://openalex.org/W2890985056","https://openalex.org/W2890527859","https://openalex.org/W2204507128","https://openalex.org/W7212562850","https://openalex.org/W7154500986","https://openalex.org/W2123771260","https://openalex.org/W2123201979","https://openalex.org/W7150819879","https://openalex.org/W7099056863","https://openalex.org/W4312433901"],"abstract_inverted_index":{"We":[0,131],"develop":[1],"a":[2,82,117,121,134,138,144],"theory":[3],"of":[4,14,24,47,90,125,141],"linear":[5],"Mahler":[6,79],"systems":[7,28],"in":[8,58,92,108,128,147],"several":[9,27,86],"variables":[10],"from":[11],"the":[12,22,41,51,56,74,77],"perspective":[13],"transcendence":[15],"and":[16,114,120,137],"algebraic":[17,123],"independence,":[18],"which":[19],"also":[20,44,132],"includes":[21],"possibility":[23],"dealing":[25],"with":[26,30],"associated":[29],"sufficiently":[31],"independent":[32,94,111],"matrix":[33],"transformations.":[34],"Our":[35],"main":[36,61],"results":[37,67],"go":[38],"far":[39],"beyond":[40],"existing":[42],"literature,":[43],"surpassing":[45],"those":[46],"two":[48,109],"unpublished":[49],"preprints":[50],"authors":[52],"made":[53],"available":[54],"on":[55,73],"arXiv":[57],"2018.":[59],"The":[60],"new":[62,118,135],"feature":[63],"is":[64],"that":[65,100],"our":[66],"apply":[68],"now":[69],"without":[70],"any":[71],"restriction":[72],"matrices":[75],"defining":[76],"corresponding":[78],"systems.":[80],"As":[81],"consequence,":[83],"we":[84,98,115],"settle":[85],"problems":[87],"concerning":[88],"expansions":[89],"numbers":[91],"multiplicatively":[93,110],"bases.":[95],"For":[96],"instance,":[97],"prove":[99],"no":[101],"irrational":[102],"real":[103],"number":[104],"can":[105],"be":[106],"automatic":[107],"integer":[112],"bases,":[113],"give":[116],"proof":[119,136],"broad":[122],"generalization":[124,140],"Cobham's":[126],"theorem":[127],"automata":[129],"theory.":[130],"provide":[133],"multivariate":[139],"Nishioka's":[142],"theorem,":[143],"landmark":[145],"result":[146],"Mahler's":[148],"method.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2020-12-21T00:00:00"}
