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<p>Let <i>k</i> ⩾ 3 be an integer. We investigate the distribution of divisors of <i>k</i>-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.</p>

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DDT theorem over k-free numbers in short intervals

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Ruiyang Liu,
  • Tingting Wen

摘要

Let k ⩾ 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.