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arXiv · 1704.04831

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

Sary Drappeau·Andrew Granville·Xuancheng Shao
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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 $(q,a_1a_2)=1$.

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Sary Drappeau, Andrew Granville, Xuancheng Shao. 2017-04-16. Smooth-supported multiplicative functions in arithmetic progressions beyond the $x^{1/2}$-barrier. https://doi.org/10.1112/s0025579317000225

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