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arXiv · 2412.16675

Hyperbolic summation involving certain arithmetic functions and the integer part function

Meselem Karras
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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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Meselem Karras. 2024-12-21. Hyperbolic summation involving certain arithmetic functions and the integer part function. https://arxiv.org/abs/2412.16675

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