The Erdős discrepancy problem over the squarefree and cubefree integers

2019/08/29 by Marco Aymone, Aymone, Marco · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1908.10997

openalex publication_date 2019/08/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let g:ℕ→\-1,1\ be a completely multiplicative function, μ be the Möbius function and μ₂²(n) be the indicator that n is cubefree. We prove that f=μ²g and f=μ₂²g 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 Erdős discrepancy problem.

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