On Some Sums Involving Small Arithmetic Functions  

作　　者：Wen Guang ZHAI 

机构地区：[1]Department of Mathematics,China University of Mining and Technology,Beijing 100083,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第10期2497-2518,共22页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11971476)。

摘　　要：Let f be any arithmetic function and define S_(f)(x):=Σ_(n≤x)f([x/n]).If the function f is small,namely,f(n)﹤﹤n^(ε),then the error term E_(f)(x)in the asymptotic formula of S_f(x)has the form O(x^(1/2+ε)).In this paper,we shall study the mean square of E_(f)(x)and establish some new results of E_(f)(x)for some special functions.

关 键 词：Small arithmetic function exponential sum asymptotic formula 

分 类 号：O174[理学—数学]