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Keywords:
arcsine law; Selberg-Delange method; $k$-free number; Dirichlet series
arcsine law; Selberg-Delange method; $k$-free number; Dirichlet series
Summary:
Let $k\geq 3$ be an integer. We investigate the distribution of divisors of $k$-free numbers using the Selberg-Delange method. We establish that the Cesàro mean of distribution functions converges uniformly to the arcsine law in short intervals. This generalizes the Deshouillers-Dress-Tenenbaum (DDT) theorem.
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