Explicit bounds for large gaps between squarefree integers

Angel Kumchev; Wade McCormick; Nathan McNew; Ariana Park; Russell Scherr; Willow Ziehr

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arXiv · 2211.09975

Explicit bounds for large gaps between squarefree integers

Angel Kumchev·Wade McCormick·Nathan McNew·Ariana Park·Russell Scherr·Willow Ziehr

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Abstract

We obtain explicit forms of the current best known asymptotic upper bounds for gaps between squarefree integers. In particular we show, for any $x \ge 2$, that every interval of the form $(x, x + 11x^{1/5}\log x]$ contains a squarefree integer. The constant 11 can be improved further, if $x$ is assumed to be larger than a (very) large constant.

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BibTeX RIS

Angel Kumchev, Wade McCormick, Nathan McNew, Ariana Park, Russell Scherr, Willow Ziehr. 2022-11-18. Explicit bounds for large gaps between squarefree integers. https://arxiv.org/abs/2211.09975

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