On the mean value of the index of composition of an integral ideal (II)

JOURNAL OF NUMBER THEORY

卷:133

Article

Zhang, Deyu¹  Zhai, Wenguang² 

[1] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Shandong, Peoples R China

[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China

关键词: Index of composition;    Asymptotic formula;    Prime ideal;   

DOI  :  10.1016/j.jnt.2012.09.003

来源: Elsevier

【 摘 要 】

Text. For each integral ideal u, let lambda(u) := log N(u)/log gamma(u) be the index of composition of u, where gamma(u) = Pi(beta vertical bar u) N(beta) and N(u) is the norm of ideal 21. In this paper, we obtain a new asymptotic formula of the sum Sigma(N(u)<= x)lambda(-k)(u). Furthermore, we improve the error term under the Generalized Riemann Hypothesis. Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=Iy3QwXo5GeU. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free