Note on the number of integral ideals in Galois extensions

被引：10

作者：

Lue GuangShi ^{[1
]}

Wang YongHui ^{[2
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[2] Capital Normal Univ, Dept Math, Beijing 100048, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2010年 / 53卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Dedekind zeta-function; integral ideal; congruences; FIELDS;

D O I：

10.1007/s11425-010-4091-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K be an algebraic number field of finite degree over the rational filed Q. Let a(k) be the number of integral ideals in K with norm k. In this paper we study the l-th integral power sum of a(k), i.e., Sigma(k <= x) a(k)(l) (l = 2, 3,...). We are able to improve the classical result of Chandrasekharan and Good. As an application we consider the number of solutions of polynomial congruences.

引用

页码：2417 / 2424

页数：8

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