Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski, 2
Volume 202 / 2022
Acta Arithmetica 202 (2022), 185-194
MSC: Primary 11A25; Secondary 11N36, 11N37.
DOI: 10.4064/aa210216-6-7
Published online: 20 December 2021
Abstract
Denote by $[t]$ the integral part of $t$. Under some simple hypothesis on the growth of the arithmetic function $f$, we prove asymptotic formulas for $$ S_f(x):= \sum _{n\le x} f\left (\left [\frac {x}{n}\right ]\right ) $$ as $x\to \infty $. The improve some recent results of Bordellès–Dai–Heyman–Pan–Shparlinski and of Zhai.
