$M(x)=o(x)$ Estimates for Beurling numbers
Number Theory
2019-11-22 v1
Abstract
In classical prime number theory there are several asymptotic formulas said to be "equivalent" to the PNT. One is the bound for the sum function of the Moebius function. For Beurling generalized numbers, this estimate is not an unconditional consequence of the PNT. Here we give two conditions that yield the Beurling version of the bound, and examples illustrating failures when these conditions are not satisfied.
Cite
@article{arxiv.1609.03504,
title = {$M(x)=o(x)$ Estimates for Beurling numbers},
author = {Gregory Debruyne and Harold G. Diamond and Jasson Vindas},
journal= {arXiv preprint arXiv:1609.03504},
year = {2019}
}
Comments
14 pages