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

Abstract

We show that smooth-supported multiplicative functions $f$ are well-distributed in arithmetic progressions $a_1{a}_2^{-1}(\mathrm{mod}q)$ on average over moduli $q\le x^{3/5-\epsilon }$ with $(q,a_1{a}_2)=1$.

23 pages

Cited by in corpus (2)

• Multiplicative functions in short arithmetic progressions
• Smooth numbers in arithmetic progressions to large moduli