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On a sum involving general arithmetic functions and the integral part function (2205.08773v2)
Published 18 May 2022 in math.NT
Abstract: Let $f$ be an arithmetic function satisfying some simple conditions. The aim of this paper is to establish an asymptotical formula for the quantity [ S_f(x):=\sum_{n\leq x}\frac{f([x/n])}{[x/n]} ] as $x\rightarrow\infty$, where $[t]$ is the integral part of the real number $t$. This generalizes some recent results of Bordell`es, Dai, Heyman, Pan and Shparlinski.