Let f and g be 1-bounded multiplicative functions for which fg = 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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Published in Forum of Mathematics, Sigma, v. 6, e15, p. 1-23.

© The Author(s) 2018

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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.

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