{"id":"https://openalex.org/W1997590243","doi":"https://doi.org/10.1090/s0025-5718-04-01632-1","title":"On quadratic fields with large 3-rank","display_name":"On quadratic fields with large 3-rank","publication_year":2004,"publication_date":"2004-01-30","ids":{"openalex":"https://openalex.org/W1997590243","doi":"https://doi.org/10.1090/s0025-5718-04-01632-1","mag":"1997590243"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01632-1","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["1088-6842","0025-5718"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"publisher-specific-oa","version":"acceptedVersion","is_accepted":true,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1090/s0025-5718-04-01632-1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086114586","display_name":"Karim Belabas","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"University of Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Karim Belabas","raw_affiliation_string":"Universit\u00c3\u00a9 Paris-Sud, D\u00c3\u00a9partement de Math\u00c3\u00a9matiques (b\u00c3\u00a2t. 425), F-91405 Orsay, France","raw_affiliation_strings":["Universit\u00c3\u00a9 Paris-Sud, D\u00c3\u00a9partement de Math\u00c3\u00a9matiques (b\u00c3\u00a2t. 425), F-91405 Orsay, France"]}],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086114586"],"corresponding_institution_ids":["https://openalex.org/I102197404"],"apc_list":null,"apc_paid":null,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":22,"cited_by_percentile_year":{"min":89,"max":90},"biblio":{"volume":"73","issue":"248","first_page":"2061","last_page":"2074"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Moduli Theory","score":0.9998,"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 Moduli Theory","score":0.9998,"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":"Proofs of Langlands Conjectures for GL(n)","score":0.9985,"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"}},{"id":"https://openalex.org/T11130","display_name":"Cryptography and Error-Correcting Codes","score":0.9985,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"keyword":"quadratic fields","score":0.6826}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6465576},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.4772037},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4589542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40943754},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40320078},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3794561},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08089626},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01632-1","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["1088-6842","0025-5718"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"publisher-specific-oa","version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.4232","pdf_url":"http://www.math.u-bordeaux1.fr/~belabas/pub/r3.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01632-1","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["1088-6842","0025-5718"],"is_oa":false,"is_in_doaj":false,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"publisher-specific-oa","version":"acceptedVersion","is_accepted":true,"is_published":false},"sustainable_development_goals":[{"score":0.65,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"grants":[],"referenced_works_count":16,"referenced_works":["https://openalex.org/W199639369","https://openalex.org/W1491984802","https://openalex.org/W1496801598","https://openalex.org/W2032354641","https://openalex.org/W2034609813","https://openalex.org/W2046261001","https://openalex.org/W2066187694","https://openalex.org/W2075469879","https://openalex.org/W2158480122","https://openalex.org/W2159366854","https://openalex.org/W2489377303","https://openalex.org/W4230453864","https://openalex.org/W4243646308","https://openalex.org/W4245342345","https://openalex.org/W4246431636","https://openalex.org/W4254599801"],"related_works":["https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2625833328"],"ngrams_url":"https://api.openalex.org/works/W1997590243/ngrams","abstract_inverted_index":{"Davenport":[0],"and":[1,12,35,117,221,429],"Heilbronn":[2],"defined":[3],"a":[4,27,271],"bijection":[5],"between":[6],"classes":[7,13],"of":[8,14,30,44,304,308,364],"binary":[9],"cubic":[10,15,71],"forms":[11],"fields,":[16],"which":[17],"has":[18],"been":[19],"used":[20],"to":[21,77,311,490],"tabulate":[22],"the":[23,37,42,45,291,326,371,471],"latter.":[24],"We":[25],"give":[26],"simpler":[28],"proof":[29],"their":[31],"theorem":[32],"then":[33],"analyze":[34],"improve":[36],"table-building":[38],"algorithm.":[39],"It":[40],"computes":[41,290],"multiplicities":[43],"":[47,79,94,120,165,224,276,293,313,334,374,390,433,478,492],"":[55,102,133,184,240,344,444],"":[56,84,103,134,185,241,281,297,318,345,378,402,445,482,496],"":[57,104,135,186,242,346,403,446],"O":[58,105,136,187,243,349],"(":[60,107,138,189,245,351,409,453],"X":[61,85,108,140,190,193,249,319],"stretchy=\"false\">)":[63,110,152,210,261,354,415,461],"":[64,111,147,149,153,200,202,207,211,256,258,262,355,420,451,462],"O(X)":[66,113],"":[67,88,114,156,218,267,285,301,322,360,382,426,467,486,500],"":[68,89,115,157,219,268,286,302,323,361,383,427,468,487,501],"":[69,90,116,220,269,324,362,384,469],"general":[70],"discriminants":[72],"(real":[73],"or":[74,159],"imaginary)":[75],"up":[76,310],"X\">":[83,317],"encoding=\"application/x-tex\">X":[87,321],"in":[91,162],"time":[92,163,328],"space":[118,222],"Superscript":[128,176,235],"3":[129,394],"slash":[130,178,181,237],"4":[131,179],"Baseline":[132,180,239],"":[139,192,248],"":[142,145,195,198,205,251,254,448],"3":[143,298,406,483],"/":[146,199,206,255],"4":[148,201,419],"":[150,203,259],"encoding=\"application/x-tex\">O(X^{3/4})":[155],",":[158,428],"more":[160],"generally":[161],"plus":[173,232,339],"7":[177],"M":[183,231,338],"+":[191,247,348],"7":[196],"M":[208,246,282,347],"encoding=\"application/x-tex\">O(X":[213],"+":[214,265,358],"X^{7/4}":[215],"/":[216],"M)":[217],"1":[236,343],"2":[238],"1":[252,352],"2":[257],"encoding=\"application/x-tex\">O(M":[264],"X^{1/2})":[266],"for":[270],"freely":[272],"chosen":[273],"positive":[274],"M\">":[280],"encoding=\"application/x-tex\">M":[284],".":[287,502],"A":[288],"variant":[289],"alttext=\"3\">":[296,481],"encoding=\"application/x-tex\">3":[300,485],"-ranks":[303],"all":[305],"quadratic":[306,386,474],"fields":[307,387],"discriminant":[309],"with":[325,388,476],"same":[327],"complexity,":[329],"but":[330],"using":[331],"only":[332],"encoding=\"application/x-tex\">M":[357],"O(1)":[359],"units":[363],"storage.":[365],"As":[366],"an":[367],"application":[368],"we":[369],"obtain":[370],"first":[372],"alttext=\"1618\">":[377],"1618":[379],"encoding=\"application/x-tex\">1618":[381],"real":[385],"alttext=\"r":[393],"normal":[396],"Delta":[398],"right-parenthesis":[399],"greater-than-or-equal-to":[400],"4\">":[401],"":[404],"r":[405],"":[407],"\u0394":[413],"\u2265":[418,457],"encoding=\"application/x-tex\">r_3(\\Delta":[422],")":[423],"\\geq":[424],"4":[425],"prove":[430],"that":[431],"alttext=\"double-struck":[436],"Q":[438],"StartRoot":[440],"negative":[441],"5393946914743":[442],"EndRoot":[443],"mathvariant=\"double-struck\">Q":[450],"":[454],"\u2212