A New Strategy for Riemann Hypothesis

Abstract

A square-free integer is a positive integer that is not divisible by the square of any prime. Merten's function, $M(x)$ is defined as the difference between the number of square free integers with an even number of prime factors and the number of those with an odd number of prime factors up to $x$. It's well known that $M(x)=O(x^{1/2+\epsilon})$ is equivalent to Riemann Hypothesis. In this paper, we derive a new equation involving Merten's function that leads to a promising technique for Riemann Hypothesis.