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Hyperbolic summation involving certain arithmetic functions and the integer part function (2412.16675v1)

Published 21 Dec 2024 in math.NT

Abstract: Let f be an arithmetic function satisfying certain conditions. In this paper, we give an asymptotic formula for the sum [\sum_{n_1 n_2 \cdots n_r \leq x} f\left(\left\lfloor \frac{x}{n_1 n_2 \cdots n_r} \right\rfloor\right), \quad r \geq 2.], where $\lfloor . \rfloor$ denotes the integer part function.

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