Title: Bombieri-Vinogradov for multiplicative functions, and beyond the $x^{1/2}$-barrier,
Abstract: Part-and-parcel of the study of "multiplicative number theory" is the study
of the distribution of multiplicative functions in arithmetic progressions.
Although appropriate analogies to the Bombieri-Vingradov Theorem have been
proved for particular examples of multiplicative functions, there has not
previously been headway on a general theory; seemingly none of the different
proofs of the Bombieri-Vingradov Theorem for primes adapt well to this
situation. In this article we find out why such a result has been so elusive,
and discover what can be proved along these lines and develop some limitations.
For a fixed residue class $a$ we extend such averages out to moduli $\leq
x^{\frac {20}{39}-\delta}$.