We investigate the distribution of the digits of quotients of randomly chosen positive integers taken from the interval $[1,T]$ , improving the previously known error term for the counting function as $T\to +\infty $ . We also resolve some natural variants of the problem concerning points with prime coordinates and points that are visible from the origin.

中文翻译：

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关于整数和素数的商的位数分布

我们研究了从区间 $[1,T]$ 中随机选择的正整数的商位数的分布，将先前已知的计数函数的误差项改进为 $T\to +\infty $ 。我们还解决了有关具有主要坐标的点和从原点可见的点的问题的一些自然变体。