Bounds of the Mertens Function

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.

9 Pages, 19 References, 10 Figures

References in corpus (1)

• Computing the Mertens function on a GPU