{"id":"https://openalex.org/W2048200915","doi":"https://doi.org/10.2178/jsl/1120224732","title":"A Schanuel condition for Weierstrass equations","display_name":"A Schanuel condition for Weierstrass equations","publication_year":2005,"publication_date":"2005-06-01","ids":{"openalex":"https://openalex.org/W2048200915","doi":"https://doi.org/10.2178/jsl/1120224732","mag":"2048200915"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1120224732","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1120224732","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/646AC5C526F522116F4EFED6C486AC81/S0022481200007118a.pdf/div-class-title-a-schanuel-condition-for-weierstrass-equations-div.pdf","source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/646AC5C526F522116F4EFED6C486AC81/S0022481200007118a.pdf/div-class-title-a-schanuel-condition-for-weierstrass-equations-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102762781","display_name":"Jonathan Kirby","orcid":"https://orcid.org/0000-0003-4031-9107"},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB","SK"],"is_corresponding":true,"raw_author_name":"Jonathan Kirby","raw_affiliation_strings":["Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB., UK, E-mail:","Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB., UK, E-mail: kirby@maths.ox.ac.uk, URL: http/www.maths.ox.ac.uk~kirby"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB., UK, E-mail:","institution_ids":["https://openalex.org/I4210120676"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB., UK, E-mail: kirby@maths.ox.ac.uk, URL: http/www.maths.ox.ac.uk~kirby","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102762781"],"corresponding_institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210120676"],"apc_list":null,"apc_paid":null,"fwci":1.2551,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.77579494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"70","issue":"2","first_page":"631","last_page":"638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9983999729156494,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9962999820709229,"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/statement","display_name":"Statement (logic)","score":0.6853033900260925},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.6741330027580261},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.664330244064331},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6245357394218445},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4191591143608093},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3807724416255951},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36923468112945557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34025269746780396},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13616636395454407},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07248273491859436},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.05119973421096802}],"concepts":[{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.6853033900260925},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6741330027580261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.664330244064331},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6245357394218445},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4191591143608093},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3807724416255951},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36923468112945557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34025269746780396},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13616636395454407},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07248273491859436},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.05119973421096802}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/jsl/1120224732","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1120224732","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/646AC5C526F522116F4EFED6C486AC81/S0022481200007118a.pdf/div-class-title-a-schanuel-condition-for-weierstrass-equations-div.pdf","source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:ueaeprints.uea.ac.uk:34972","is_oa":true,"landing_page_url":null,"pdf_url":"https://ueaeprints.uea.ac.uk/id/eprint/34972/1/A_Schanuel_condition_for_Weierstrass.pdf","source":{"id":"https://openalex.org/S4306400384","display_name":"UEA Digital Repository (University of East Anglia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1118541","host_organization_name":"University of East Anglia","host_organization_lineage":["https://openalex.org/I1118541"],"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":"PeerReviewed"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1120224732","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1120224732","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:ora.ox.ac.uk:uuid:96c5786c-28fa-43c3-ba5c-9fc2ec35d1d0","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:96c5786c-28fa-43c3-ba5c-9fc2ec35d1d0","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.2178/jsl/1120224732","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1120224732","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/646AC5C526F522116F4EFED6C486AC81/S0022481200007118a.pdf/div-class-title-a-schanuel-condition-for-weierstrass-equations-div.pdf","source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2048200915.pdf","grobid_xml":"https://content.openalex.org/works/W2048200915.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W54296832","https://openalex.org/W1486898453","https://openalex.org/W2012829016","https://openalex.org/W2035100180","https://openalex.org/W2050070395","https://openalex.org/W2245093405","https://openalex.org/W2319921428","https://openalex.org/W2327176554","https://openalex.org/W2894650977","https://openalex.org/W4237180828","https://openalex.org/W4253001479"],"related_works":["https://openalex.org/W2475705533","https://openalex.org/W186129870","https://openalex.org/W3200522959","https://openalex.org/W4389944781","https://openalex.org/W2997993211","https://openalex.org/W120415280","https://openalex.org/W4383099232","https://openalex.org/W167088980","https://openalex.org/W1993275793","https://openalex.org/W2253954117"],"abstract_inverted_index":{"Abstract":[0],"I":[1],"prove":[2],"a":[3,15],"version":[4],"of":[5,17],"Schanuel's":[6],"conjecture":[7],"for":[8],"Weierstrass":[9],"equations":[10],"in":[11,26],"differential":[12],"fields,":[13],"answering":[14],"question":[16],"Zilber,":[18],"and":[19],"show":[20],"that":[21],"the":[22,27],"linear":[23],"independence":[24],"condition":[25],"statement":[28],"cannot":[29],"be":[30],"relaxed.":[31]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}