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

被引：18
|
作者：
Sun, Qingfeng [1 ]
Zhang, Deyu [2 ]
机构：
[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
来源：
JOURNAL OF NUMBER THEORY | 2016年 / 168卷
基金：
中国国家自然科学基金;
关键词：
Triple divisor function; Ternary quadratic form; Twisted character sum; NUMBER;
D O I：
10.1016/j.jnt.2016.04.010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
引用
收藏
页码：215 / 246
页数：32
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