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arXiv · 1908.10997

The Erd\H{o}s discrepancy problem over the squarefree and cubefree integers

Marco Aymone
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Abstract

Let $g:\mathbb{N}\to\{-1,1\}$ be a completely multiplicative function, $\mu$ be the M\"obius function and $\mu_2^2(n)$ be the indicator that $n$ is cubefree. We prove that $f=\mu^2g$ and $f=\mu_2^2g$ have unbounded partial sums. Our proofs are built upon Klurman and Mangerel's proof of Chudakov's conjecture, Klurman's work on correlations of multiplicative functions and Tao's resolution of the Erd\H{o}s discrepancy problem.

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Marco Aymone. 2019-08-29. The Erd\H{o}s discrepancy problem over the squarefree and cubefree integers. https://arxiv.org/abs/1908.10997

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