The distribution of r-free numbers in arithmetic progressions

TL;DR

This paper extends the understanding of r-free numbers by establishing an upper bound similar to the Bombieri-Vinogradov theorem for their distribution in arithmetic progressions.

Contribution

It generalizes previous results by Orr, providing a new upper bound for r-free numbers in arithmetic progressions.

Findings

Established an upper bound of Bombieri-Vinogradov type for r-free numbers

Generalized Orr's earlier work on the distribution of r-free numbers

Enhanced understanding of the distribution of r-free numbers in arithmetic progressions

Abstract

A positive integer n is called r-free if n is not divisible by the r-th power of a prime. Generalizing earlier work of Orr, we provide an upper bound of Bombieri-Vinogradov type for the r-free numbers in arithmetic progressions.