Hyperbolic summation for fractional sums

DOI10.4064/AA230331-31-7arXiv2212.05443OpenAlexW4386690360MaRDI QIDQ6071878

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Publication date: 29 November 2023

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Abstract: Let $f(n)$ be an arithmetic function with $f(n)ll{n}^{a}lpha$ for some $alphain[0,1)$ and let $lfloor.floor$ denote the integer part function. In this paper, we evaluate asymptotically the sums ${\displaystyle }$sum_{n_{1}n_{2}leq x}f left( leftlfloor frac{x}{n_{1}n_{2}} ight floor ight),${\displaystyle }$ we use the estimation of three-dimensional exponential sums due to Robert and Sargos.

Full work available at URL: https://arxiv.org/abs/2212.05443

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