关于Q(4k^(2n)+1)的理想类群的循环子群  

On the Cyclic Subgroups of the Ideal Class Group of Q(4k^(2n)+1)

作　　者：陈宏基[1] 

机构地区：[1]惠州大学数学系,惠州516015

出　　处：《数学学报（中文版）》1999年第6期1135-1139,共5页Acta Mathematica Sinica：Chinese Series

摘　　要：设ｄ，ａ，ｋ，ｎ是适合４ｋ２ｎ＋１＝ｄａ２，ｋ＞１，ｎ＞２，ｄ无平方因子的正整数；又设Ｃ（Ｋ）和ｈ（Ｋ）分别是实二次域Ｋ的理想类群和类数．本文证明了：当ａ＜０．５ｋ０．５６ｎ时，则ｈ（ｋ）＝０（ｍｏｄｎ）和Ｃ（Ｋ）必有ｎ阶循环子群．Let d, a, k, n be the positive integers such that 4k2n + 1 = da2, k > 1, n > 2and d is square free. Further let C(K) and h(K) denote the ideal class group andclass number of the real quadratic field K = Q(W). In this paper, we prove that ifa < 0.5ho,56n, then h(K) = 0 (mod n) and C(K) has a cyclic subgroup with order n.

关 键 词：实二次域 理想类群 循环子群 类数 可除性 

分 类 号：O156.5[理学—数学]