{"title":"本源导体阿贝尔场的类数奇偶性注记，3","authors":"H. Ichimura","doi":"10.5036/mjiu.51.39","DOIUrl":null,"url":null,"abstract":"Let p be a prime number of the form p = 2 ℓ +1 with some odd prime number ℓ . For such a prime number p , it is shown that the relative class number h (cid:0) p of the p th cyclotomic (cid:12)eld Q ( (cid:16) p ) is odd when 2 remains prime in Q ( (cid:16) ℓ ) + by Estes [3], Stevenhagen [11] and Mets(cid:127)ankyl(cid:127)a [8] using a Bernoulli number associated to Q ( (cid:16) p ). In this note, we give an alternative proof of the assertion using a cyclotomic unit of Q ( (cid:16) p ) + .","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"88 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Note on class number parity of an abelian field of prime conductor, III\",\"authors\":\"H. Ichimura\",\"doi\":\"10.5036/mjiu.51.39\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let p be a prime number of the form p = 2 ℓ +1 with some odd prime number ℓ . For such a prime number p , it is shown that the relative class number h (cid:0) p of the p th cyclotomic (cid:12)eld Q ( (cid:16) p ) is odd when 2 remains prime in Q ( (cid:16) ℓ ) + by Estes [3], Stevenhagen [11] and Mets(cid:127)ankyl(cid:127)a [8] using a Bernoulli number associated to Q ( (cid:16) p ). In this note, we give an alternative proof of the assertion using a cyclotomic unit of Q ( (cid:16) p ) + .\",\"PeriodicalId\":18362,\"journal\":{\"name\":\"Mathematical Journal of Ibaraki University\",\"volume\":\"88 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Journal of Ibaraki University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/mjiu.51.39\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Ibaraki University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/mjiu.51.39","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Note on class number parity of an abelian field of prime conductor, III
Let p be a prime number of the form p = 2 ℓ +1 with some odd prime number ℓ . For such a prime number p , it is shown that the relative class number h (cid:0) p of the p th cyclotomic (cid:12)eld Q ( (cid:16) p ) is odd when 2 remains prime in Q ( (cid:16) ℓ ) + by Estes [3], Stevenhagen [11] and Mets(cid:127)ankyl(cid:127)a [8] using a Bernoulli number associated to Q ( (cid:16) p ). In this note, we give an alternative proof of the assertion using a cyclotomic unit of Q ( (cid:16) p ) + .
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