A New Equation Involving Merten's Function And It's Implications

Irfan Okay

Published 2017-12-05Version 1

One of the many equivalent statements for Riemann Hypothesis is that Merten's function $M(x)$, which is related to square free integers, is of order $O(x^{1/2+\epsilon})$. In this paper, we derive an exact equation involving Merten's function, which leads to a promising new technique for obtaining a nontrivial bound for $M(x)$.