Sums of the triple divisor function over values of a ternary quadratic form

JOURNAL OF NUMBER THEORY

卷:168

Article

Sun, Qingfeng¹  Zhang, Deyu² 

[1] Shandong Univ, Sch Math & Stat, Weihai 264209, Shandong, Peoples R China

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

关键词: Triple divisor function;    Ternary quadratic form;    Twisted character sum;   

DOI  :  10.1016/j.jnt.2016.04.010

来源: Elsevier

【 摘 要 】

Let tau(3)(n) be the triple divisor function which is the number of solutions of the equation d(1)d(2)d(3) = n in natural numbers. It is shown that Sigma(1 <= n1,n2.n3 <=root x) tau(3)(n(1)(2) + n(2)(2) + n(3)(2)) = c(1)x(3/2)(log x)(2) + c(2)x(3/2) log x + c(3)x(3/2) + O-epsilon(x(11/8+epsilon)) for some constants c(1), c(2) and c(3). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free