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

## TL;DR

This paper demonstrates that smooth-supported multiplicative functions are well-distributed in arithmetic progressions for moduli up to nearly x^{3/5}, surpassing the traditional x^{1/2} barrier.

## Contribution

It extends the distribution results of multiplicative functions in arithmetic progressions beyond the classical square-root barrier.

## Key findings

- Distribution holds for moduli up to x^{3/5- ext{epsilon}}
- Results apply to smooth-supported multiplicative functions
- Distribution is on average over moduli q

## 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 $(q,a_1a_2)=1$.