{"id":"https://openalex.org/W1973605968","doi":"https://doi.org/10.1090/s0025-5718-05-01811-9","title":"CM-fields with relative class number one","display_name":"CM-fields with relative class number one","publication_year":2005,"publication_date":"2005-11-29","ids":{"openalex":"https://openalex.org/W1973605968","doi":"https://doi.org/10.1090/s0025-5718-05-01811-9","mag":"1973605968"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01811-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01811-9","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01811-9/S0025-5718-05-01811-9.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/2006-75-254/S0025-5718-05-01811-9/S0025-5718-05-01811-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053397463","display_name":"Geon-No Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Geon-No Lee","raw_affiliation_strings":["Department of Mathematics Education, Korea University, 136-701, Seoul, Korea","Department of Mathematics Education, Korea University, 136-701 Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Korea University, 136-701, Seoul, Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics Education, Korea University, 136-701 Seoul, Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114027199","display_name":"Soun-Hi Kwon","orcid":null},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Soun-Hi Kwon","raw_affiliation_strings":["Department of Mathematics Education, Korea University, 136-701, Seoul, Korea","Department of Mathematics Education, Korea University, 136-701 Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Korea University, 136-701, Seoul, Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics Education, Korea University, 136-701 Seoul, Korea","institution_ids":["https://openalex.org/I197347611"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053397463"],"corresponding_institution_ids":["https://openalex.org/I197347611"],"apc_list":null,"apc_paid":null,"fwci":2.1037,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8521692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"75","issue":"254","first_page":"997","last_page":"1013"},"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/T10304","display_name":"Geometric and Algebraic Topology","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/T10849","display_name":"Finite Group Theory Research","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/algorithm","display_name":"Algorithm","score":0.6523811221122742},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.5476521253585815},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.42529845237731934},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42068976163864136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3855913281440735},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.382305383682251},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.07428285479545593}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6523811221122742},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.5476521253585815},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.42529845237731934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42068976163864136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3855913281440735},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.382305383682251},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07428285479545593},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-05-01811-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01811-9","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01811-9/S0025-5718-05-01811-9.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:10.1.1.154.2488","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2488","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/2006-75-254/S0025-5718-05-01811-9/S0025-5718-05-01811-9.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01811-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01811-9","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01811-9/S0025-5718-05-01811-9.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1973605968.pdf","grobid_xml":"https://content.openalex.org/works/W1973605968.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W23855251","https://openalex.org/W261064270","https://openalex.org/W299502923","https://openalex.org/W587082047","https://openalex.org/W1558606648","https://openalex.org/W1579490422","https://openalex.org/W1663136107","https://openalex.org/W1911894398","https://openalex.org/W1964630909","https://openalex.org/W1976923416","https://openalex.org/W1992416585","https://openalex.org/W2007714401","https://openalex.org/W2010828369","https://openalex.org/W2012000314","https://openalex.org/W2025601576","https://openalex.org/W2033723664","https://openalex.org/W2040685037","https://openalex.org/W2049626822","https://openalex.org/W2055000659","https://openalex.org/W2081348809","https://openalex.org/W2100521236","https://openalex.org/W2117805174","https://openalex.org/W2120761354","https://openalex.org/W2212866430","https://openalex.org/W2322852486","https://openalex.org/W2323709746","https://openalex.org/W4292101538","https://openalex.org/W6601015854","https://openalex.org/W6688359729"],"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"],"abstract_inverted_index":{"We":[0],"will":[1],"show":[2],"that":[3],"the":[4,39,44,76,140,172,183],"normal":[5,45,109,178],"CM-fields":[6,46,77,110,179],"with":[7,47,78,132],"relative":[8,48],"class":[9,49,79,133,173],"number":[10,50,80,134,174],"one":[11,51,81,135,175],"are":[12,52,82,136],"of":[13,53,83,111,143],"degrees":[14,54,84,112],"<inline-formula":[15,55,85,113,145,158],"content-type=\"math/mathml\">":[16,56,86,114,146,159],"<mml:math":[17,57,87,115,147,160],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18,58,88,116,148,161],"alttext=\"less-than-or-equal-to":[19,59,89,117],"216\">":[20],"<mml:semantics>":[21,61,91,119,150,163],"<mml:mrow>":[22,62,92,120],"<mml:mo>":[23,63,93,121],"\u2264":[24,64,94,122],"</mml:mo>":[25,65,95,123],"<mml:mn>216</mml:mn>":[26],"</mml:mrow>":[27,67,97,125],"<mml:annotation":[28,68,98,126,152,165],"encoding=\"application/x-tex\">\\leq":[29,69,99,127],"216</mml:annotation>":[30],"</mml:semantics>":[31,71,101,129,154,167],"</mml:math>":[32,72,102,130,155,168],"</inline-formula>":[33,73,103,131,156,169],".":[34,104,170],"Moreover,":[35],"if":[36],"we":[37],"assume":[38],"Generalized":[40,184],"Riemann":[41,185],"Hypothesis,":[42],"then":[43],"96\">":[60,118],"<mml:mn>96</mml:mn>":[66,124,164],"96</mml:annotation>":[70,128],",":[74],"and":[75],"104\">":[90],"<mml:mn>104</mml:mn>":[96],"104</mml:annotation>":[100],"By":[105],"many":[106],"authors":[107],"all":[108],"known":[137],"except":[138,187],"for":[139,177,188],"possible":[141],"fields":[142],"degree":[144],"alttext=\"64\">":[149],"<mml:mn>64</mml:mn>":[151],"encoding=\"application/x-tex\">64</mml:annotation>":[153],"or":[157],"alttext=\"96\">":[162],"encoding=\"application/x-tex\">96</mml:annotation>":[166],"Consequently":[171],"problem":[176],"is":[180],"solved":[181],"under":[182],"Hypothesis":[186],"these":[189],"two":[190],"cases.":[191]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
