English

Bounds of the Mertens Function

General Mathematics 2021-04-19 v3

Abstract

In this paper, we derive new properties of the Mertens function and discuss a likely upper bound of the absolute value of the Mertens function logx!>M(x)\sqrt{\log{x!}}>|M(x)| when x>1x>1. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.

Keywords

Cite

@article{arxiv.2012.11756,
  title  = {Bounds of the Mertens Function},
  author = {Darrell Cox and Sourangshu Ghosh and Eldar Sultanow},
  journal= {arXiv preprint arXiv:2012.11756},
  year   = {2021}
}

Comments

9 Pages, 19 References, 10 Figures

R2 v1 2026-06-23T21:10:39.754Z