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arXiv · 2205.12108

Variance of Squarefull Numbers in Short Intervals

Tsz Ho Chan
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Abstract

In this paper, we study the variance of the number of squarefull numbers in short intervals. As a result, we are able to prove that, for any $0 < θ< 1/2$, almost all short intervals $(x, x + x^{1/2 + θ}]$ contain about $\frac{ζ(3/2)}{2 ζ(3)} x^θ$ squarefull numbers.

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Tsz Ho Chan. 2023-09-19. Variance of Squarefull Numbers in Short Intervals. https://arxiv.org/abs/2205.12108

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