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arXiv · 1512.00149

Variance of $\mathcal{B}$-free integers in short intervals

Maria Avdeeva
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Abstract

We prove some new statements on the distribution of $\mathcal{B}$-free numbers in short intervals. In particular, we show an asymptotic result for the variance of the number of $\mathcal{B}$-free integers in random short intervals which are, in some sense, uniformly distributed. We establish a connection between our work and the paper by El Abdalaoui, Lemańczyk & de la Rue on a flow associated to $\mathcal{B}$-free integers. In addition, we study an analog of our variance for $k$-free integers in a number field which provides new information for the corresponding dynamical system constructed by Cellarosi & Vinogradov.

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Maria Avdeeva. 2015-12-01. Variance of $\mathcal{B}$-free integers in short intervals. https://arxiv.org/abs/1512.00149

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