On the estimate $M(x)=o(x)$ for Beurling generalized numbers
Number Theory
2025-06-10 v2
Abstract
We show that the sum function of the M\"{o}bius function of a Beurling number system must satisfy the asymptotic bound 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.
Cite
@article{arxiv.2406.00736,
title = {On the estimate $M(x)=o(x)$ for Beurling generalized numbers},
author = {Jasson Vindas},
journal= {arXiv preprint arXiv:2406.00736},
year = {2025}
}
Comments
9 pages