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.
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)
