Divisibility of class numbers of non-normal totally real cubic number fields

被引：0
|
作者：
Lee, Jungyun [1 ]
机构：
[1] Korea Adv Inst Sci & Technol, Dept Math Sci, ASARC, Taejon 350701, South Korea
来源：
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2010年 / 86卷 / 02期
基金：
新加坡国家研究基金会;
关键词：
Class number; totally real cubic fields; IDEAL CLASS-GROUPS;
D O I：
10.3792/pjaa.86.38
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider a family of cubic fields {K-m}(m >= 4) associated to the irreducible cubic polynomials P-m(x) = x(3) - mx(2) - (m+1)x - 1, (m >= 4). We prove that there are infinitely many {K-m}(m >= 4)'s whose class numbers are divisible by a given integer n. From this, we find that there are infinitely many non-normal totally real cubic fields with class number divisible by any given integer n.
引用
收藏
页码：38 / 40
页数：3
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