On the Error Term for the Number of Integral Ideals in Galois Extensions

Sanying Shi^1,

¹School of Mathematics, Hefei University of Technology, Hefei, China

Cite this paper:
Sanying Shi. On the Error Term for the Number of Integral Ideals in Galois Extensions. Turkish Journal of Analysis and Number Theory. 2014; 2(6):230-232. doi: 10.12691/tjant-2-6-8

Abstract

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 Δ(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 Δ(x) is given. This result constitutes an improvement upon that of Lü and Wang for the error terms in mean value.

Keywords:
dedekind zeta-function dirichlet series mean value

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