{"id":"https://openalex.org/W2076738856","doi":"https://doi.org/10.1090/s0025-5718-08-02169-8","title":"On the computation of class numbers of real abelian fields","display_name":"On the computation of class numbers of real abelian fields","publication_year":2008,"publication_date":"2008-10-14","ids":{"openalex":"https://openalex.org/W2076738856","doi":"https://doi.org/10.1090/s0025-5718-08-02169-8","mag":"2076738856"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02169-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02169-8","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02169-8/S0025-5718-08-02169-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02169-8/S0025-5718-08-02169-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033138536","display_name":"Tuomas Hakkarainen","orcid":null},"institutions":[{"id":"https://openalex.org/I183173800","display_name":"Turku Centre for Computer Science","ror":"https://ror.org/00vy7ed73","country_code":"FI","type":"facility","lineage":["https://openalex.org/I130217899","https://openalex.org/I155660961","https://openalex.org/I183173800"]},{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Tuomas Hakkarainen","raw_affiliation_strings":["Department of Mathematics & TUCS, Turku Centre for Computer Science, University of Turku, FI-20014 Turku, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics & TUCS, Turku Centre for Computer Science, University of Turku, FI-20014 Turku, Finland","institution_ids":["https://openalex.org/I183173800","https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033138536"],"corresponding_institution_ids":["https://openalex.org/I155660961","https://openalex.org/I183173800"],"apc_list":null,"apc_paid":null,"fwci":0.4479,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.64376425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"78","issue":"265","first_page":"555","last_page":"555"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9842000007629395,"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"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9836000204086304,"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":0.8938112258911133},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6915597915649414},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6454324722290039},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.6189682483673096},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5863887071609497},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5488345623016357},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5156549215316772},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.5047928094863892},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.5014982223510742},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.44784632325172424},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3610621988773346},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33216506242752075},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32992449402809143},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11662071943283081},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05714207887649536}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8938112258911133},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6915597915649414},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6454324722290039},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.6189682483673096},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5863887071609497},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5488345623016357},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5156549215316772},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.5047928094863892},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.5014982223510742},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.44784632325172424},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3610621988773346},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33216506242752075},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32992449402809143},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11662071943283081},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05714207887649536},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","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":5,"locations":[{"id":"doi:10.1090/s0025-5718-08-02169-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02169-8","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02169-8/S0025-5718-08-02169-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.134.6478","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.6478","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tu-berlin.de/~kant/ants/Poster/Hakkarainen_Poster.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.6581","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.6581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2009-78-265/S0025-5718-08-02169-8/S0025-5718-08-02169-8.pdf","raw_type":"text"},{"id":"pmh:oai:www.doria.fi:10024/33586","is_oa":false,"landing_page_url":"http://www.doria.fi/handle/10024/33586","pdf_url":null,"source":{"id":"https://openalex.org/S4377196760","display_name":"Doria (University of Helsinki)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I133731052","host_organization_name":"University of Helsinki","host_organization_lineage":["https://openalex.org/I133731052"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Doctoral dissertation (monograph)"},{"id":"pmh:oai:www.utupub.fi:10024/33586","is_oa":false,"landing_page_url":"http://www.utupub.fi/handle/10024/33586","pdf_url":null,"source":{"id":"https://openalex.org/S4306402470","display_name":"UTUPub (University of Turku)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I155660961","host_organization_name":"University of Turku","host_organization_lineage":["https://openalex.org/I155660961"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"fi=Monografiav\u00e4it\u00f6skirja|en=Doctoral dissertation (monograph)|"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02169-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02169-8","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02169-8/S0025-5718-08-02169-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2076738856.pdf","grobid_xml":"https://content.openalex.org/works/W2076738856.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W31134417","https://openalex.org/W182598722","https://openalex.org/W264413169","https://openalex.org/W297994758","https://openalex.org/W599421205","https://openalex.org/W1558606648","https://openalex.org/W1571682270","https://openalex.org/W1594529635","https://openalex.org/W1994203327","https://openalex.org/W1998529728","https://openalex.org/W2000286442","https://openalex.org/W2000368716","https://openalex.org/W2010858206","https://openalex.org/W2014032471","https://openalex.org/W2019228100","https://openalex.org/W2019924527","https://openalex.org/W2021335688","https://openalex.org/W2035683672","https://openalex.org/W2040769892","https://openalex.org/W2061202173","https://openalex.org/W2064556072","https://openalex.org/W2073454809","https://openalex.org/W2075036292","https://openalex.org/W2076738856","https://openalex.org/W2159366854","https://openalex.org/W2576804572","https://openalex.org/W3043060850","https://openalex.org/W3044631666","https://openalex.org/W3094850882","https://openalex.org/W4213309192","https://openalex.org/W4230326723","https://openalex.org/W4242328316","https://openalex.org/W4246109111","https://openalex.org/W4292101538","https://openalex.org/W6600632366","https://openalex.org/W6600992289","https://openalex.org/W6640106245","https://openalex.org/W6640346001"],"related_works":["https://openalex.org/W4299849194","https://openalex.org/W1541818783","https://openalex.org/W3123755168","https://openalex.org/W2110732483","https://openalex.org/W2181825851","https://openalex.org/W2621885661","https://openalex.org/W2331449017","https://openalex.org/W4293568303","https://openalex.org/W3013448869","https://openalex.org/W2795448197"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"give":[4],"a":[5,21],"procedure":[6],"to":[7,46,61],"search":[8],"for":[9],"prime":[10,51,62],"divisors":[11,52],"of":[12,15,23,36,38],"class":[13,34],"numbers":[14,35],"real":[16],"abelian":[17],"fields":[18,37],"and":[19],"present":[20],"table":[22],"odd":[24],"primes":[25],"$<10000$":[26],"not":[27],"dividing":[28],"the":[29,33],"degree":[30],"that":[31,48],"divide":[32],"conductor":[39],"$\\leq":[40],"2000$.":[41],"Cohen\u00e2\u0080\u0093Lenstra":[42],"heuristics":[43],"allow":[44],"us":[45],"conjecture":[47],"no":[49],"larger":[50],"should":[53],"exist.":[54],"Previous":[55],"computations":[56],"have":[57],"been":[58],"largely":[59],"limited":[60],"power":[63],"conductors.":[64]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
