{"id":"https://openalex.org/W1975040579","doi":"https://doi.org/10.1215/00294527-2143853","title":"Modular Ax\u2013Lindemann\u2013Weierstrass with Derivatives","display_name":"Modular Ax\u2013Lindemann\u2013Weierstrass with Derivatives","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1975040579","doi":"https://doi.org/10.1215/00294527-2143853","mag":"1975040579"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2143853","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-2143853","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","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/A5061066962","display_name":"Jonathan Pila","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jonathan Pila","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061066962"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1309,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.93141076,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"54","issue":"3-4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9994999766349792,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9987999796867371,"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/weierstrass-functions","display_name":"Weierstrass functions","score":0.8785637617111206},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7244255542755127},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.716143786907196},{"id":"https://openalex.org/keywords/elliptic-function","display_name":"Elliptic function","score":0.6568201184272766},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6396778225898743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5480407476425171},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49545514583587646},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47983595728874207},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4591594934463501},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.4443580210208893},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3356729745864868},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24487951397895813},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17173796892166138},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05333465337753296}],"concepts":[{"id":"https://openalex.org/C65945562","wikidata":"https://www.wikidata.org/wiki/Q3075283","display_name":"Weierstrass functions","level":2,"score":0.8785637617111206},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7244255542755127},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.716143786907196},{"id":"https://openalex.org/C123958593","wikidata":"https://www.wikidata.org/wiki/Q938102","display_name":"Elliptic function","level":2,"score":0.6568201184272766},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6396778225898743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5480407476425171},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49545514583587646},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47983595728874207},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4591594934463501},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.4443580210208893},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3356729745864868},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24487951397895813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17173796892166138},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05333465337753296},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1215/00294527-2143853","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00294527-2143853","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1376053779","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1376053779","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:cfb00a01-729f-4578-a4d0-147d92c41a1d","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:cfb00a01-729f-4578-a4d0-147d92c41a1d","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":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1294628090","display_name":null,"funder_award_id":"EP/I01893X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1559103132","https://openalex.org/W1585954501","https://openalex.org/W1988479350","https://openalex.org/W2006796395","https://openalex.org/W2010757891","https://openalex.org/W2016516249","https://openalex.org/W2021586952","https://openalex.org/W2034692503","https://openalex.org/W2035100180","https://openalex.org/W2077062072","https://openalex.org/W2087810928","https://openalex.org/W2091615812","https://openalex.org/W2096287896","https://openalex.org/W2098043063","https://openalex.org/W2101327550","https://openalex.org/W2162052349","https://openalex.org/W2167031861","https://openalex.org/W2170395672","https://openalex.org/W2322894077","https://openalex.org/W2327176554","https://openalex.org/W2947837230","https://openalex.org/W3099403682","https://openalex.org/W3100897720","https://openalex.org/W4237293924","https://openalex.org/W4237551483","https://openalex.org/W4239679971"],"related_works":["https://openalex.org/W2285265598","https://openalex.org/W4293090968","https://openalex.org/W3102092488","https://openalex.org/W4304192652","https://openalex.org/W1967780741","https://openalex.org/W142781213","https://openalex.org/W4366375474","https://openalex.org/W3159211351","https://openalex.org/W3082081268","https://openalex.org/W2064106489"],"abstract_inverted_index":{"In":[0],"a":[1],"recent":[2],"paper":[3],"I":[4,20],"established":[5],"an":[6],"analogue":[7],"of":[8,12],"the":[9,15],"Lindemann\u2013Weierstrass":[10],"part":[11],"Ax\u2013Schanuel":[13],"for":[14],"elliptic":[16,39],"modular":[17],"function.":[18],"Here":[19],"extend":[21],"this":[22],"to":[23],"include":[24],"its":[25],"first":[26],"and":[27,37],"second":[28],"derivatives.":[29],"A":[30],"generalization":[31],"is":[32],"given":[33],"that":[34],"includes":[35],"exponential":[36],"Weierstrass":[38],"functions":[40],"as":[41],"well.":[42]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}