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.
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A.G. has received funding from the European Research Council grant agreement no 670239, and from NSERC Canada under the CRC program. X.S. was supported by a Glasstone Research Fellowship.
Granville, Andrew and Shao, Xuancheng, "When Does the Bombieri–Vinogradov Theorem Hold for a Given Multiplicative Function?" (2018). Mathematics Faculty Publications. 35.