WHEN DOES THE BOMBIERI–VINOGRADOV THEOREM HOLD FOR A GIVEN MULTIPLICATIVE FUNCTION?. (24th August 2018) - GRANVILLE, ANDREW; SHAO, XUANCHENG
Abstract : Let $f$ and $g$ be 1-bounded multiplicative functions for which $f* g=1_{.=1}$ . 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.