Abstract

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., Σk⩽αakl(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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