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arXiv · 2012.11756

Bounds of the Mertens Function

Darrell Cox·Sourangshu Ghosh·Eldar Sultanow
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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 $\sqrt{\log{x!}}>|M(x)|$ when $x>1$. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.

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Darrell Cox, Sourangshu Ghosh, Eldar Sultanow. 2020-12-22. Bounds of the Mertens Function. https://doi.org/10.31219/osf.io/86whq

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