Hyperbolic summation for fractional sums
Volume 211 / 2023
Acta Arithmetica 211 (2023), 185-192
MSC: Primary 60G50; Secondary 11H06, 11N37.
DOI: 10.4064/aa230331-31-7
Published online: 12 September 2023
Abstract
Let $\tau (n)$ denote the number of positive divisors of an integer $n\geq 1$ and let $\lfloor \cdot \rfloor $ denote the integer part function. We evaluate asymptotically the sums $$ \sum _{n\leq x}f (\lfloor x/n\rfloor )\tau (n), $$ where $f$ is an arithmetic function satisfying mild growth conditions.
