{"title":"关于切环场族的极大实子域的类数","authors":"M. Ram","doi":"10.21136/CMJ.2023.0364-22","DOIUrl":null,"url":null,"abstract":"For any square-free positive integer m ≡ 10 (mod 16) with m ⩾ 26, we prove that the class number of the real cyclotomic field ℚ(ζ4m +ζ4m−1) is greater than 1, where ζ4m is a primitive 4mth root of unity.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"937 - 940"},"PeriodicalIF":0.4000,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the class number of the maximal real subfields of a family of cyclotomic fields\",\"authors\":\"M. Ram\",\"doi\":\"10.21136/CMJ.2023.0364-22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any square-free positive integer m ≡ 10 (mod 16) with m ⩾ 26, we prove that the class number of the real cyclotomic field ℚ(ζ4m +ζ4m−1) is greater than 1, where ζ4m is a primitive 4mth root of unity.\",\"PeriodicalId\":50596,\"journal\":{\"name\":\"Czechoslovak Mathematical Journal\",\"volume\":\"73 1\",\"pages\":\"937 - 940\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-04-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Czechoslovak Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/CMJ.2023.0364-22\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Czechoslovak Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/CMJ.2023.0364-22","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the class number of the maximal real subfields of a family of cyclotomic fields
For any square-free positive integer m ≡ 10 (mod 16) with m ⩾ 26, we prove that the class number of the real cyclotomic field ℚ(ζ4m +ζ4m−1) is greater than 1, where ζ4m is a primitive 4mth root of unity.
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