Smooth-supported multiplicative functions in arithmetic progressions beyond the $x^{1/2}$-barrier (1704.04831v2)

Abstract: We show that smooth-supported multiplicative functions $f$ are well-distributed in arithmetic progressions $a_1a_2^{-1} \pmod q$ on average over moduli $q\leq x^{3/5-\varepsilon}$ with $(q,a_1a_2)=1$.