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

Andrew Granville; Sary Drappeau; Xuancheng Shao

arxiv: 1704.04831 · v2 · pith:YBT5A5HYnew · submitted 2017-04-16 · 🧮 math.NT

Smooth-supported multiplicative functions in arithmetic progressions beyond the x^(1/2)-barrier

Sary Drappeau , Andrew Granville , Xuancheng Shao This is my paper

classification 🧮 math.NT

keywords arithmeticfunctionsmultiplicativeprogressionssmooth-supportedaveragebarrierbeyond

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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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Smooth-supported multiplicative functions in arithmetic progressions beyond the x^(1/2)-barrier

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