{"id":"https://openalex.org/W3095758124","doi":"https://doi.org/10.1007/s10958-020-05093-5","title":"Multiplication and Division on Elliptic Curves, Torsion Points, and Roots of Modular Equations","display_name":"Multiplication and Division on Elliptic Curves, Torsion Points, and Roots of Modular Equations","publication_year":2020,"publication_date":"2020-10-30","ids":{"openalex":"https://openalex.org/W3095758124","doi":"https://doi.org/10.1007/s10958-020-05093-5","mag":"3095758124"},"language":"en","primary_location":{"id":"doi:10.1007/s10958-020-05093-5","doi":"https://doi.org/10.1007/s10958-020-05093-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10958-020-05093-5","pdf_url":null,"source":{"id":"https://openalex.org/S83211391","display_name":"Journal of Mathematical Sciences","issn_l":"1072-3374","issn":["1072-3374","1072-1964","1573-8795"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Sciences","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5046980582","display_name":"Semjon F. Adlaj","orcid":"https://orcid.org/0000-0003-4219-7836","observed_orcids":["https://orcid.org/0000-0003-4219-7836"]},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I4405258151","display_name":"Federal Research Center \u201cComputer Science and Control\u201d of the Russian Academy of Sciences","ror":"https://ror.org/006wm7015","country_code":"RU","type":"government","lineage":["https://openalex.org/I4405258151"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. Adlaj","raw_affiliation_strings":["Federal Research Center \u201cInformatics and Control\u201d of the Russian Academy of Sciences, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Federal Research Center \u201cInformatics and Control\u201d of the Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I4405258151"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046980582"],"corresponding_institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I4405258151"],"apc_list":{"value":3490,"currency":"USD","value_usd":3490},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20981273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"251","issue":"3","first_page":"315","last_page":"338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.5830000042915344,"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":0.5830000042915344,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.3801000118255615,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.009600000455975533,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/elliptic-curves","display_name":"elliptic curves","score":0.972000002861023},{"id":"https://openalex.org/keywords/elliptic-functions","display_name":"elliptic functions","score":0.7480000257492065},{"id":"https://openalex.org/keywords/modular-equations","display_name":"modular equations","score":0.7319999933242798},{"id":"https://openalex.org/keywords/arithmetic-geometric-mean","display_name":"arithmetic-geometric mean","score":0.8029999732971191},{"id":"https://openalex.org/keywords/lemniscate-of-bernoulli","display_name":"lemniscate of Bernoulli","score":0.9210000038146973},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.6430000066757202},{"id":"https://openalex.org/keywords/riemann-sphere","display_name":"Riemann sphere","score":0.527999997138977}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7924690842628479},{"id":"https://openalex.org/C80146680","wikidata":"https://www.wikidata.org/wiki/Q2654923","display_name":"Complex multiplication","level":3,"score":0.7215335965156555},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6651875972747803},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.6167502999305725},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.551506519317627},{"id":"https://openalex.org/C73683783","wikidata":"https://www.wikidata.org/wiki/Q2728886","display_name":"Modular elliptic curve","level":4,"score":0.5127021074295044},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5111883282661438},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.5068250298500061},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.5005433559417725},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.4746038317680359},{"id":"https://openalex.org/C59766168","wikidata":"https://www.wikidata.org/wiki/Q3001220","display_name":"Modular curve","level":3,"score":0.46263617277145386},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4434356689453125},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.43054527044296265},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.427554726600647},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4210672974586487},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.19746559858322144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12577617168426514},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10958-020-05093-5","doi":"https://doi.org/10.1007/s10958-020-05093-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10958-020-05093-5","pdf_url":null,"source":{"id":"https://openalex.org/S83211391","display_name":"Journal of Mathematical Sciences","issn_l":"1072-3374","issn":["1072-3374","1072-1964","1573-8795"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1585954501","https://openalex.org/W2015996198","https://openalex.org/W2036116198","https://openalex.org/W2165118609","https://openalex.org/W2277535877","https://openalex.org/W2928381868","https://openalex.org/W2948436716","https://openalex.org/W6636334347","https://openalex.org/W6684365232"],"related_works":["https://openalex.org/W4240211410","https://openalex.org/W7095614789","https://openalex.org/W4320351168","https://openalex.org/W2087325864","https://openalex.org/W4416697813","https://openalex.org/W2036231525","https://openalex.org/W2048410410","https://openalex.org/W1529471319","https://openalex.org/W2328813493","https://openalex.org/W2597019336"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2020-11-09T00:00:00"}