On the parity of the class number of the 7nth cyclotomic field
On the parity of the class number of the 7nth cyclotomic field
复制标题
论第7n分圆域类数的奇偶性
DOI：
10.2478/s12175-009-0132-5
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发表时间：
2009
影响因子：
1.6
通讯作者：
H. Ichimura
中科院分区：
文献类型：
--
作者：
H. Ichimura
对奇素数p和≥ 0的整数n，设hn是pn+1阶分圆域Q（$）的类数
\zeta _{p^{n + 1} }
$$).已知当p = 3或5时，对于所有n ≥ 0，hn是奇数。我们证明了当p = 7时也是如此。
AbstractFor an odd prime number p and an integer n ≥ 0, let hn be the class number of the pn+1st cyclotomic field Q($$
\zeta _{p^{n + 1} }
$$). It is known that when p = 3 or 5, hn is odd for all n ≥ 0. We prove that the same holds also when p = 7.