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arXiv · 2511.17539

Variations and extensions of Croft's problem

Sophia Smyrli
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Abstract

In this work we study the following classical still challenging Calculus problem: {\it If $f:(0,\infty)\to\mathbb{R}$ is a continuous function, for which the sequence $\{f(nx)\}$ tends to zero, for every positive $x$, as $n$ tends to infinity, then $f(x)$ also tends to zero, as $x$ tends to infinity.}

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Sophia Smyrli. 2025-11-07. Variations and extensions of Croft's problem. https://arxiv.org/abs/2511.17539

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