A Bombieri-Vinogradov-type theorem for moduli with small radical

TL;DR

This paper extends a Bombieri-Vinogradov-type theorem to sparser sets of moduli with small radicals, broadening understanding of prime distribution in arithmetic progressions.

Contribution

It generalizes previous results by combining methods to handle larger and sparser moduli with small radicals, advancing prime distribution analysis.

Findings

Extended Bombieri-Vinogradov theorem to moduli with small radicals

Achieved results for moduli up to x^{1/3- ext{epsilon}}

Combined previous methods with Baker's theorem for general moduli

Abstract

In this article, we extend our recent work on a Bombieri-Vinogradov-type theorem for sparse sets of prime powers $p^N\le x^{1/4-\varepsilon}$ with $p\le (\log x)^C$ to sparse sets of moduli $s\le x^{1/3-\varepsilon}$ with radical rad$(s)\le x^{9/40}$. To derive our result, we combine our previous method with a Bombieri-Vinogradov-type theorem for general moduli $s\le x^{9/40}$ obtained by Roger Baker.