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arXiv · 2406.00736

On the estimate $M(x)=o(x)$ for Beurling generalized numbers

Jasson Vindas
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Abstract

We show that the sum function of the M\"{o}bius function of a Beurling number system must satisfy the asymptotic bound $M(x)=o(x)$ if it satisfies the prime number theorem and its prime distribution function arises from a monotone perturbation of either the classical prime numbers or the logarithmic integral.

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Jasson Vindas. 2024-06-02. On the estimate $M(x)=o(x)$ for Beurling generalized numbers. https://doi.org/10.1007/s10476-024-00061-6

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