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arXiv · 2208.05589

Certain floor function sums over powers

Joshua Stucky
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Abstract

We study the sums $$ S_f(x) = \sum_{n\leq x} f\left(\left\lfloor\frac{x}{n}\right\rfloor\right) $$ when $f$ is supported on $r$th powers with $r\geq 2$. This restriction allows us to give nontrivial estimates for one of the error terms in the asymptotic expansion of $S_f(x)$. We also state several conjectures related to our results.

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Joshua Stucky. 2022-08-10. Certain floor function sums over powers. https://arxiv.org/abs/2208.05589

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