A Bombieri–Vinogradov-type theorem for moduli with small radical
Volume 211 / 2023
Acta Arithmetica 211 (2023), 173-184
MSC: Primary 11N13; Secondary 11N36.
DOI: 10.4064/aa221211-1-9
Published online: 31 October 2023
Abstract
In this article, we extend our recent work on a Bombieri–Vinogradov-type theorem for sparse sets of prime powers $p^N\leqslant x^{1/4-\varepsilon }$ with $p\leqslant (\log x)^C$ to sparse sets of moduli $s\leqslant x^{1/3-\varepsilon }$ with radical rad$(s)\leqslant x^{9/40}$. To derive our result, we combine our previous method with a Bombieri–Vinogradov-type theorem for general moduli $s\leqslant x^{9/40}$ obtained by Roger Baker.
