When does the Bombieri-Vinogradov Theorem hold for a given multiplicative function?

Abstract

Let $f$ and $g$ be $1$-bounded multiplicative functions for which $f\ast g=1_{.=1}$. The Bombieri-Vinogradov Theorem holds for both $f$ and $g$ if and only if the Siegel-Walfisz criterion holds for both $f$ and $g$, and the Bombieri-Vinogradov Theorem holds for $f$ restricted to the primes.

19 pages

References in corpus (1)

• Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers