On a sum involving small arithmetic function and the integral part function

被引：1
|
作者：
Li, Jiamin [1 ]
Ma, Jing [1 ]
机构：
[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China
来源：
JOURNAL OF NUMBER THEORY | 2023年 / 247卷
基金：
中国国家自然科学基金;
关键词：
Asymptotic formula; Multiple exponential sums; Mobius transformation; Integral part function;
D O I：
10.1016/j.jnt.2022.12.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let f be a "small" arithmetic function in the sense that f = g *1 and g(n) << n-j, where j is a fixed non-negative number. In this paper, we study the sum Sigma(n <= x) f([x/n])/[x/n](k) as x -> infinity, where [center dot] denotes the integral part function and k is a fixed non-negative number. Our results generalize the very recent work of Stucky, also combine and generalize the original two types of sums studied by Bordelles-Dai-Heyman-Pan-Shparlinski. (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：35 / 45
页数：11
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