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arXiv · 1604.04481

A note on multiplicative functions on progressions to large moduli

Ben Green
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Abstract

Let $f : \mathbf{N} \rightarrow \mathbf{C}$ be a bounded multiplicative function. Let $a$ be a fixed integer (say $a = 1$). Then $f$ is well-distributed on the progression $n \equiv a \pmod{q} \subset \{1,\dots, X\}$, for almost all primes $q \in [Q,2Q]$, for $Q$ as large as $X^{\frac{1}{2} + \frac{1}{78} - o(1)}$.

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Ben Green. 2016-04-15. A note on multiplicative functions on progressions to large moduli. https://arxiv.org/abs/1604.04481

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