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Heath-Brown D. R., The number of Abelian groups of order at most x, Journtes Arithmttiques, Luminy 1989.

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Article

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

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


Turkish Journal of Analysis and Number Theory. 2014, Vol. 2 No. 6, 230-232
DOI: 10.12691/tjant-2-6-8
Copyright © 2014 Science and Education Publishing

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.

Correspondence to: Sanying  Shi, School of Mathematics, Hefei University of Technology, Hefei, China. Email: vera123_99@hotmail.com

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.

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