{"title":"关于固定素数上理想类的奇偶性","authors":"Jeongho Park","doi":"10.1353/ajm.2020.0003","DOIUrl":null,"url":null,"abstract":"abstract:For real quadratic number fields, we consider the order of ideal classes of split prime ideals, $P$, whose norm is a fixed rational prime. We collect fundamental discriminants satisfying a trivial condition for $P$ to be principal, and show that for a positive density of such discriminants, the cyclic subgroup of the ideal class group generated by $P$ does not have a 2-part.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2020-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2020.0003","citationCount":"2","resultStr":"{\"title\":\"On the parity of ideal classes over a fixed prime\",\"authors\":\"Jeongho Park\",\"doi\":\"10.1353/ajm.2020.0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"abstract:For real quadratic number fields, we consider the order of ideal classes of split prime ideals, $P$, whose norm is a fixed rational prime. We collect fundamental discriminants satisfying a trivial condition for $P$ to be principal, and show that for a positive density of such discriminants, the cyclic subgroup of the ideal class group generated by $P$ does not have a 2-part.\",\"PeriodicalId\":7453,\"journal\":{\"name\":\"American Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2020-01-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1353/ajm.2020.0003\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1353/ajm.2020.0003\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2020.0003","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
abstract:For real quadratic number fields, we consider the order of ideal classes of split prime ideals, $P$, whose norm is a fixed rational prime. We collect fundamental discriminants satisfying a trivial condition for $P$ to be principal, and show that for a positive density of such discriminants, the cyclic subgroup of the ideal class group generated by $P$ does not have a 2-part.
期刊介绍：
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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