The average behavior of the coefficients of Dedekind zeta function over square numbers

JOURNAL OF NUMBER THEORY

卷:131

Article

Lue, Guangshi¹  Yang, Zhishan¹ 

[1] Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China

关键词: Coefficients of Dedekind zeta function;    Galois field;    Divisor problem;   

DOI  :  10.1016/j.jnt.2011.01.018

来源: Elsevier

【 摘 要 】

In this paper, we are interested in the average behavior of the coefficients of Dedekind zeta function over square numbers. In Galois fields of degree d which is odd, when l >= 1 is an integer, we have Sigma(n <= x)a(n(2))(l) = xP(m) (logx) + O(x(1)-3/md+6+epsilon), where m = ((d + 1)/2)(l)d(l-1), P(m)(t) is a polynomial in t of degree m - 1, and epsilon > 0 is an arbitrarily small constant. By using our method, we also rectify the main terms of the k-dimensional divisor problem in some Galois fields over square numbers established by Deza and Varukhina (2008) [DV]. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free