2015/12/01 by Maria Avdeeva, Avdeeva, Maria
Mathematics · #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.1512.00149
arxiv created 2015/12/01 · openalex publication_date 2015/12/01 · arxiv updated 2015/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove some new statements on the distribution of B-free numbers in short intervals. In particular, we show an asymptotic result for the variance of the number of 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 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.