{"id":"https://openalex.org/W2091712624","doi":"https://doi.org/10.1112/s1461157014000345","title":"Subexponential class group and unit group computation in large degree number fields","display_name":"Subexponential class group and unit group computation in large degree number fields","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2091712624","doi":"https://doi.org/10.1112/s1461157014000345","mag":"2091712624"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157014000345","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157014000345","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4387ACB036E3358143A563F196E386CB/S1461157014000345a.pdf/div-class-title-subexponential-class-group-and-unit-group-computation-in-large-degree-number-fields-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4387ACB036E3358143A563F196E386CB/S1461157014000345a.pdf/div-class-title-subexponential-class-group-and-unit-group-computation-in-large-degree-number-fields-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030566023","display_name":"Jean\u2010Fran\u00e7ois Biasse","orcid":"https://orcid.org/0000-0001-8591-8408"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jean-Fran\u00e7ois Biasse","raw_affiliation_strings":["Computer Science Department and Mathematics Department, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada email","Computer Science Department and Mathematics Department, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4,Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department and Mathematics Department, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada email","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Computer Science Department and Mathematics Department, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4,Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025858070","display_name":"Claus Fieker","orcid":"https://orcid.org/0000-0002-3420-1498"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Claus Fieker","raw_affiliation_strings":["University of Kaiserslautern, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern, Germany email","University of Kaiserslautern, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern,Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern, Germany email","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"University of Kaiserslautern, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern,Germany","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.6907,"has_fulltext":true,"cited_by_count":42,"citation_normalized_percentile":{"value":0.97292382,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"17","issue":"A","first_page":"385","last_page":"403"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9975000023841858,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8946641087532043},{"id":"https://openalex.org/keywords/ideal-class-group","display_name":"Ideal class group","score":0.8113675117492676},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7463197708129883},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.7246324419975281},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.7063398361206055},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5683804750442505},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5511981844902039},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5229347944259644},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5226097702980042},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5160417556762695},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4882541000843048},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4633728861808777},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40463680028915405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14027008414268494},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10612747073173523}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8946641087532043},{"id":"https://openalex.org/C8367249","wikidata":"https://www.wikidata.org/wiki/Q912083","display_name":"Ideal class group","level":3,"score":0.8113675117492676},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7463197708129883},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.7246324419975281},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.7063398361206055},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5683804750442505},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5511981844902039},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5229347944259644},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5226097702980042},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5160417556762695},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4882541000843048},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4633728861808777},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40463680028915405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14027008414268494},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10612747073173523},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/s1461157014000345","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157014000345","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4387ACB036E3358143A563F196E386CB/S1461157014000345a.pdf/div-class-title-subexponential-class-group-and-unit-group-computation-in-large-degree-number-fields-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1112/s1461157014000345","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157014000345","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4387ACB036E3358143A563F196E386CB/S1461157014000345a.pdf/div-class-title-subexponential-class-group-and-unit-group-computation-in-large-degree-number-fields-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2091712624.pdf","grobid_xml":"https://content.openalex.org/works/W2091712624.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W139993337","https://openalex.org/W197145066","https://openalex.org/W1486771829","https://openalex.org/W1501162952","https://openalex.org/W1531368347","https://openalex.org/W1541224886","https://openalex.org/W1557027117","https://openalex.org/W1575598731","https://openalex.org/W1578625033","https://openalex.org/W1596400416","https://openalex.org/W1969728959","https://openalex.org/W1979160832","https://openalex.org/W1980735577","https://openalex.org/W1989510734","https://openalex.org/W2011809718","https://openalex.org/W2025623851","https://openalex.org/W2036532467","https://openalex.org/W2069046788","https://openalex.org/W2071271934","https://openalex.org/W2075323532","https://openalex.org/W2096556656","https://openalex.org/W2096941982","https://openalex.org/W2126483728","https://openalex.org/W2133465710","https://openalex.org/W2142778315","https://openalex.org/W2160639384","https://openalex.org/W2168975319","https://openalex.org/W2369713881","https://openalex.org/W3103256322","https://openalex.org/W3157578321","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2006551014","https://openalex.org/W2052454793","https://openalex.org/W2032102388","https://openalex.org/W2091712624","https://openalex.org/W3023259722","https://openalex.org/W2043491846","https://openalex.org/W2999072711","https://openalex.org/W3098637024","https://openalex.org/W4285802550","https://openalex.org/W2951859153"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"describe":[2],"how":[3],"to":[4,43,56],"compute":[5],"the":[6,11,28,37,53],"ideal":[7],"class":[8],"group":[9,13],"and":[10,32],"unit":[12],"of":[14,39,46],"an":[15],"order":[16],"in":[17,21],"a":[18],"number":[19,47],"field":[20],"subexponential":[22],"time.":[23],"Our":[24],"method":[25],"relies":[26],"on":[27],"generalized":[29],"Riemann":[30],"hypothesis":[31],"other":[33],"usual":[34],"heuristics":[35],"concerning":[36],"smoothness":[38],"ideals.":[40],"It":[41],"applies":[42],"arbitrary":[44],"classes":[45],"fields,":[48],"including":[49],"those":[50],"for":[51],"which":[52],"degree":[54],"goes":[55],"infinity.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}
