On the distribution of the digits of quotients of integers and primes

TL;DR

This paper studies the distribution of digits in quotients of randomly selected integers and primes, providing improved error bounds and addressing related problems involving prime points and visibility from the origin.

Contribution

It advances understanding of digit distribution in quotients and resolves variants involving prime coordinates and visibility, with improved error estimates.

Findings

Improved error term for counting digit distributions as T increases

Results on digit distribution for quotients with prime coordinates

Analysis of points visible from the origin in related contexts

Abstract

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.