Science and Education Publishing Turkish Journal of Analysis and Number Theory 2 6 2014 12 18 On the Error Term for the Number of Integral Ideals in Galois Extensions 230 232 EN Sanying Shi School of Mathematics, Hefei University of Technology, Hefei, China TJANT2014268 10.12691/tjant-2-6-8 2014 11 25 2014 12 05 2014 12 18 Suppose that E is an algebraic number field over the rational field Let a(n) be the number of integral ideals in E with norm n and (x) denote the remainder term in the asymptotic formula of the l-th integral power sum of a(n). In this paper the bound of the average behavior of (x) is given. This result constitutes an improvement upon that of Lü and Wang for the error terms in mean value.