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Bounds of the Mertens Function

Published 22 Dec 2020 in math.GM | (2012.11756v3)

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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