{"id":"https://openalex.org/W2012012533","doi":"https://doi.org/10.1007/bf02393650","title":"\u00dcber Rationale Punkte auf Kurven Dritter Ordnung vom Geschlechte Eins","display_name":"\u00dcber Rationale Punkte auf Kurven Dritter Ordnung vom Geschlechte Eins","publication_year":1948,"publication_date":"1948-01-01","ids":{"openalex":"https://openalex.org/W2012012533","doi":"https://doi.org/10.1007/bf02393650","mag":"2012012533"},"language":"de","primary_location":{"id":"doi:10.1007/bf02393650","doi":"https://doi.org/10.1007/bf02393650","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02393650","pdf_url":"https://projecteuclid.org/journals/acta-mathematica/volume-80/issue-none/%c3%9cber-Rationale-Punkte-auf-Kurven-Dritter-Ordnung-vom-Geschlechte-Eins/10.1007/BF02393650.pdf","source":{"id":"https://openalex.org/S113542759","display_name":"Acta Mathematica","issn_l":"0001-5962","issn":["0001-5962","1871-2509"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321325","host_organization_name":"Mittag-Leffler Institute","host_organization_lineage":["https://openalex.org/P4310321325"],"host_organization_lineage_names":["Mittag-Leffler Institute"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Mathematica","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/acta-mathematica/volume-80/issue-none/%c3%9cber-Rationale-Punkte-auf-Kurven-Dritter-Ordnung-vom-Geschlechte-Eins/10.1007/BF02393650.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011839935","display_name":"A. Wiman","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Wiman","raw_affiliation_strings":["Lund"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lund","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5011839935"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.18597997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"80","issue":"0","first_page":"223","last_page":"257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T11166","display_name":"Analytic Number Theory Research","score":9.999999747378752e-05,"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/rational-points-on-curves","display_name":"rational points on curves","score":0.8240000009536743},{"id":"https://openalex.org/keywords/elliptic-curves","display_name":"elliptic curves","score":0.8320000171661377},{"id":"https://openalex.org/keywords/genus-one-curves","display_name":"genus one curves","score":0.6489999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39396822452545166},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.32088011503219604}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf02393650","doi":"https://doi.org/10.1007/bf02393650","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02393650","pdf_url":"https://projecteuclid.org/journals/acta-mathematica/volume-80/issue-none/%c3%9cber-Rationale-Punkte-auf-Kurven-Dritter-Ordnung-vom-Geschlechte-Eins/10.1007/BF02393650.pdf","source":{"id":"https://openalex.org/S113542759","display_name":"Acta Mathematica","issn_l":"0001-5962","issn":["0001-5962","1871-2509"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321325","host_organization_name":"Mittag-Leffler Institute","host_organization_lineage":["https://openalex.org/P4310321325"],"host_organization_lineage_names":["Mittag-Leffler Institute"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Mathematica","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.acta/1485888481","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.acta/1485888481","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,"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":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/bf02393650","doi":"https://doi.org/10.1007/bf02393650","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02393650","pdf_url":"https://projecteuclid.org/journals/acta-mathematica/volume-80/issue-none/%c3%9cber-Rationale-Punkte-auf-Kurven-Dritter-Ordnung-vom-Geschlechte-Eins/10.1007/BF02393650.pdf","source":{"id":"https://openalex.org/S113542759","display_name":"Acta Mathematica","issn_l":"0001-5962","issn":["0001-5962","1871-2509"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321325","host_organization_name":"Mittag-Leffler Institute","host_organization_lineage":["https://openalex.org/P4310321325"],"host_organization_lineage_names":["Mittag-Leffler Institute"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Mathematica","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2012012533.pdf","grobid_xml":"https://content.openalex.org/works/W2012012533.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2588953402"],"related_works":["https://openalex.org/W2588953402","https://openalex.org/W301232886","https://openalex.org/W4240738050","https://openalex.org/W150990762","https://openalex.org/W2613079492","https://openalex.org/W1572401847","https://openalex.org/W2082986272","https://openalex.org/W603037986","https://openalex.org/W6889102755","https://openalex.org/W2004159665"],"abstract_inverted_index":{"in":[0],"LUND.I~":[1],"1.In":[2],"dieser":[3,34,137],"Arbeit":[4],"werden":[5],"immer":[6],"als":[7],"Koeffizienten":[8],"rationale":[9,133],"Zahlen":[10,92],"angenommen.Existiert":[11],"ein":[12],"rationaler":[13],"Punkt":[14],"auf":[15,26],"der":[16,50,52],"Kurve,":[17,120],"so":[18],"l~isst":[19],"sich":[20,131],"ihre":[21],"Gleichung":[22,35],"bekanntlieh":[23],"stets":[24,139],"rational":[25],"die":[27,45,124],"Gestalt":[28],"(~)":[29],"v'":[30],"=":[31],"f,(*)":[32],"reduzieren.Von":[33],"nehmen":[36],"wir":[37,61,73],"unseren":[38],"Ausgangspunkt.Es":[39],"erscheint":[40],"vorteilhaft":[41],"hier":[42,108],"nicht":[43,153],"notwendig":[44],"Weierstrassche":[46],"Normalform":[47],"anzunehmen.Je":[48],"nach":[49,75],"Rationalit~it":[51],"Wurzeln":[53],"el,":[54,82,93,100],"e~,":[55,101],"e":[56,96,102],"3":[57,97],"vonfs(x)":[58],"~-0":[59],"bekommen":[60],"drei":[62],"Fglle,":[63],"fiir":[64,158],"welche":[65],"eine":[66,89,155],"verschiedene":[67],"Behandlung":[68],"erforderlich":[69],"ist.Diese":[70],"F~ille":[71],"ordnen":[72],"bier":[74],"den":[76,91,111,159],"mit":[77],"ihnen":[78],"verbundenen":[79],"steigenden":[80],"Schwierigkeiten.I)":[81],"e.~,":[83],"e.~":[84],"sind":[85,104],"s~tmtlich":[86],"rational.2)":[87],"Nur":[88],"yon":[90,112,126,144],"e2":[94],"und":[95],"ist":[98,150],"rational.3)":[99],"8":[103],"sfimtlich":[105],"irrational.Wir":[106],"erinnern":[107],"zungchst":[109],"an":[110],"H.":[113],"POINCAR~":[114],"eingeffihrten":[115],"Begriff":[116],"yore":[117],"Range":[118],"einer":[119],"1":[121],"womit":[122],"man":[123],"Minimalzahl":[125],"Baslspunkten":[127],"bezeichnet,":[128],"aus":[129],"denen":[130],"s~imtliche":[132],"Punkte":[134],"herleiten":[135],"lassen.Dass":[136],"Rang":[138,160],"endlich":[140],"ist,":[141],"wurde":[142],"sp~tter":[143],"L.":[145],"J.":[146],"MORD~LL":[147],"bewiesen.~":[148],"Dagegen":[149],"es":[151],"noch":[152],"gelungen":[154],"obere":[156],"Grenze":[157],"zu":[161],"bestimmen.":[162]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}
