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.
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页码：2417 / 2424
页数：8
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