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arXiv · 1502.02374

A note on the Liouville function in short intervals

Kaisa Matomäki·Maksym Radziwiłł
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Abstract

In this note we give a short and self-contained proof that, for any $δ> 0$, $\sum_{x \leq n \leq x+x^δ} λ(n) = o(x^δ)$ for almost all $x \in [X, 2X]$. We also sketch a proof of a generalization of such a result to general real-valued multiplicative functions. Both results are special cases of results in our more involved and lengthy recent pre-print.

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Kaisa Matomäki, Maksym Radziwiłł. 2015-02-09. A note on the Liouville function in short intervals. https://arxiv.org/abs/1502.02374

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