ON THE PARITY OF THE CLASS NUMBER OF THE 7nTH CYCLOTOMIC FIELD

被引：4

作者：

Ichimura, Humio ^{[1
]}

机构：

[1] Ibaraki Univ, Fac Sci, Mito, Ibaraki 3108512, Japan

来源：

MATHEMATICA SLOVACA | 2009年 / 59卷 / 03期

基金：

日本学术振兴会;

关键词：

cyclotomic field; class number; parity; EXTENSIONS; ROOTS; UNITY;

D O I：

10.2478/s12175-009-0132-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an odd prime number p and an integer n >= 0, let h(n) be the class number of the p(n+1)st cyclotomic field Q(zeta(pn+1)). It is known that when p = 3 or 5, h(n) is odd for all n >= 0. We prove that the same holds also when p = 7.

引用

页码：357 / 364

页数：8

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