Note on the number of integral ideals in Galois extensions  

作　　者：L GuangShi1,& WANG YongHui2 1School of Mathematics,Shandong University,Jinan 250100,China 2Department of Mathematics,Capital Normal University,Beijing 100048,China 

出　　处：《Science China Mathematics》2010年第9期2417-2424,共8页中国科学：数学（英文版）

基　　金：supported in part by National Natural Science Foundation of China(Grant No.10701048);Natural Science Foundation of Shandong Province (Grant No.ZR2009AM007);Independent Innovation Foundation of Shandong University;supported in part by National Basic Research Program of China (973 Program) (Grant No.2007CB807902);National Natural Science Foundation of China (Grant No.10601034)

摘　　要：Let K be an algebraic number field of finite degree over the rational filed Q.Let ak be the number of integral ideals in K with norm k.In this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(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.Let K be an algebraic number field of finite degree over the rational filed Q.Let ak be the number of integral ideals in K with norm k.In this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(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.

关 键 词：DEDEKIND ZETA-FUNCTION INTEGRAL IDEAL CONGRUENCES 

分 类 号：O172.2[理学—数学]