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

2024/06/02 by Vindas, Jasson
#11N80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2406.00736

Abstract

We show that the sum function of the Möbius 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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