{"id":"https://openalex.org/W7204162947","doi":"https://doi.org/10.48550/arxiv.2608.22178","title":"Degree of irrationality of a product of two elliptic curves","display_name":"Degree of irrationality of a product of two elliptic curves","publication_year":2026,"publication_date":"2026-08-23","ids":{"openalex":"https://openalex.org/W7204162947","doi":"https://doi.org/10.48550/arxiv.2608.22178"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.22178","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22178","pdf_url":"https://arxiv.org/pdf/2608.22178","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.22178","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134894929","display_name":"Yongnam Lee","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lee, Yongnam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5134894929"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","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/T10061","display_name":"Algebraic Geometry and Number Theory","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/T12351","display_name":"Geometry and complex manifolds","score":0.0,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"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/elliptic-curves","display_name":"elliptic curves","score":0.6710000038146973},{"id":"https://openalex.org/keywords/abelian-surfaces","display_name":"abelian surfaces","score":0.9309999942779541},{"id":"https://openalex.org/keywords/rational-maps","display_name":"rational maps","score":0.7099999785423279},{"id":"https://openalex.org/keywords/plane-cubics","display_name":"plane cubics","score":0.7149999737739563},{"id":"https://openalex.org/keywords/birational-geometry","display_name":"birational geometry","score":0.6980000138282776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7853000164031982},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7838000059127808},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6021000146865845},{"id":"https://openalex.org/C2777019708","wikidata":"https://www.wikidata.org/wiki/Q1412340","display_name":"Irrationality","level":3,"score":0.4819999933242798},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.438400000333786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3912999927997589},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3578000068664551},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C138888516","wikidata":"https://www.wikidata.org/wiki/Q2266843","display_name":"Infinite product","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C201801670","wikidata":"https://www.wikidata.org/wiki/Q2132775","display_name":"Elliptic rational functions","level":4,"score":0.24570000171661377}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.22178","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22178","pdf_url":"https://arxiv.org/pdf/2608.22178","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.22178","doi":"https://doi.org/10.48550/arxiv.2608.22178","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.22178","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.22178","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22178","pdf_url":"https://arxiv.org/pdf/2608.22178","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204162947.pdf","grobid_xml":"https://content.openalex.org/works/W7204162947.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4225979773","https://openalex.org/W7204792256","https://openalex.org/W2302130443","https://openalex.org/W7207761823","https://openalex.org/W1990101925","https://openalex.org/W2979140604","https://openalex.org/W7098207538","https://openalex.org/W3040854556","https://openalex.org/W3009071782","https://openalex.org/W2097613818"],"abstract_inverted_index":{"In":[0],"this":[1],"short":[2],"paper,":[3],"we":[4],"prove":[5],"that,":[6],"for":[7],"any":[8],"two":[9],"complex":[10],"elliptic":[11],"curves":[12],"\\(E\\)":[13,36],"and":[14,37,66],"\\(F\\),":[15],"the":[16],"product":[17],"\\(E\\times":[18,48],"F\\)":[19],"has":[20],"degree":[21,52],"of":[22,35,51,63],"irrationality":[23],"\\(3\\).":[24,53],"The":[25,54],"upper":[26],"bound":[27,56],"is":[28],"obtained":[29],"from":[30,68],"compatible":[31],"cyclic":[32],"plane-cubic":[33],"models":[34],"\\(F\\):":[38],"three":[39],"diagonal":[40],"bihomogeneous":[41],"sections":[42],"define":[43],"a":[44],"dominant":[45,60],"rational":[46,61],"map":[47],"F\\dashrightarrow\\mathbb":[49],"P^2\\)":[50],"lower":[55],"follows":[57],"by":[58],"excluding":[59],"maps":[62],"degrees":[64],"\\(1\\)":[65],"\\(2\\)":[67],"an":[69],"abelian":[70],"surface":[71],"to":[72],"\\(\\mathbb":[73],"P^2\\).":[74]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-26T00:00:00"}